phd in cs usa

Email forwarding for @cs.stanford.edu is changing. Updates and details here . CS Commencement Ceremony June 16, 2024.  Learn More .

PhD Admissions

Main navigation.

The Computer Science Department PhD program is a top-ranked research-oriented program, typically completed in 5-6 years. There are very few course requirements and the emphasis is on preparation for a career in Computer Science research. 

Eligibility

To be eligible for admission in a Stanford graduate program, applicants must meet:

• Applicants from institutions outside of the United States must hold the equivalent of a United States Bachelor's degree from a college or University of recognized good standing. See detailed information by region on  Stanford Graduate Admissions website. 
• Area of undergraduate study . While we do not require a specific undergraduate coursework, it is important that applicants have strong quantitative and analytical skills; a Bachelor's degree in Computer Science is not required.

Any questions about the admissions eligibility should be directed to  [email protected] .

Application Checklist

An completed online application must be submitted by the CS Department application deadline and can be found  here .

Application Deadlines

The online application can be found here  and we will only one admissions cycle for the PhD program per respective academic term.

• Values of Inclusion
• 2020 Antiracism Task Force
• 2022 DEI Report
• Research News

Department Life

• Listed by Recipient
• Listed by Category
• Oral History of Cornell CS
• CS 40th Anniversary Booklet
• ABC Book for Computer Science at Cornell by David Gries
• Books by Author
• Books Chronologically
• The 60's
• The 70's
• The 80's
• The 90's
• The 00's
• The 2010's
• Faculty Positions: Ithaca
• Faculty Positions: New York City
• Lecturer Position: Ithaca
• Post-doc Position: Ithaca
• Staff/Technical Positions
• Ugrad Course Staff
• Ithaca Info
• Internal info
• Graduation Information
• Cornell Learning Machines Seminar
• Student Colloquium
• Spring 2024 Colloquium
• Conway-Walker Lecture Series
• Salton 2023 Lecture Series
• Spring 2024 Artificial Intelligence Seminar
• Spring 2024 Robotics Seminar
• Spring 2024 Theory Seminar
• Big Red Hacks
• Cornell University - High School Programming Contests 2024
• Game Design Initiative
• CSMore: The Rising Sophomore Summer Program in Computer Science
• Explore CS Research
• ACSU Research Night
• Cornell Junior Theorists' Workshop 2023
• Researchers
• Ph.D. Students
• M.Eng. Students
• M.S. Students
• Ph.D. Alumni
• List of Courses
• Course and Room Roster
• CS Advanced Standing Exam
• Architecture
• Artificial Intelligence
• Computational Biology
• Database Systems
• Human Interaction
• Machine Learning
• Natural Language Processing
• Programming Languages
• Scientific Computing
• Software Engineering
• Systems and Networking
• Theory of Computing
• Contact Academic Advisor
• Your First CS Course
• Technical Electives
• CS with Other Majors/Areas
• Transfer Credits
• CS Honors Program
• CPT for International CS Undergrads
• Graduation Requirements
• Useful Forms
• Becoming a CS Major
• Requirements
• Game Design Minor
• Co-op Program
• Cornell Bowers CIS Undergraduate Research Experience (BURE)
• Independent Research (CS 4999)
• Student Groups
• UGrad Events
• Undergraduate Learning Center
• UGrad Course Staff Info
• The Review Process
• Early M.Eng Credit Approval
• Financial Aid
• Prerequisites
• The Application Process
• The Project
• Pre-approved Electives
• Degree Requirements
• The Course Enrollment Process
• Advising Tips
• Entrepreneurship
• Cornell Tech Programs
• Professional Development
• Contact MEng Office
• Career Success
• Applicant FAQ
• Computer Science Graduate Office Hours
• Exam Scheduling Guidelines
• Graduate TA Handbook
• MS Degree Checklist
• MS Student Financial Support
• Special Committee Selection
• Diversity and Inclusion
• Contact MS Office
• Ph.D. Applicant FAQ
• Graduate Housing
• Non-Degree Application Guidelines
• Ph. D. Visit Day
• Business Card Policy
• Cornell Tech
• Curricular Practical Training
• Fellowship Opportunities
• Field of Computer Science Ph.D. Student Handbook
• Field A Exam Summary Form
• Graduate School Forms
• Instructor / TA Application
• Ph.D. Requirements
• Ph.D. Student Financial Support
• Travel Funding Opportunities
• Travel Reimbursement Guide
• The Outside Minor Requirement
• CS Graduate Minor
• Outreach Opportunities
• Parental Accommodation Policy
• Special Masters
• Student Spotlights
• Contact PhD Office

Search form

Computer Science Ph.D. Program

You are here.

The Cornell Ph.D. program in computer science is consistently ranked among the top six departments in the country, with world-class research covering all of computer science. Our computer science program is distinguished by the excellence of the faculty, by a long tradition of pioneering research, and by the breadth of its Ph.D. program. Faculty and Ph.D. students are located both in Ithaca and in New York City at the Cornell Tech campus . The Field of Computer Science also includes faculty members from other departments (Electrical Engineering, Information Science, Applied Math, Mathematics, Operations Research and Industrial Engineering, Mechanical and Aerospace Engineering, Computational Biology, and Architecture) who can supervise a student's Ph.D. thesis research in computer science.

Over the past years we've increased our strength in areas such as artificial intelligence, computer graphics, systems, security, machine learning, and digital libraries, while maintaining our depth in traditional areas such as theory, programming languages and scientific computing.  You can find out more about our research here . 

The department provides an exceptionally open and friendly atmosphere that encourages the sharing of ideas across all areas. 

Cornell is located in the heart of the Finger Lakes region. This beautiful area provides many opportunities for recreational activities such as sailing, windsurfing, canoeing, kayaking, both downhill and cross-country skiing, ice skating, rock climbing, hiking, camping, and brewery/cider/wine-tasting. In fact, Cornell offers courses in all of these activities.

The Cornell Tech campus in New York City is located on Roosevelt Island.  Cornell Tech  is a graduate school conceived and implemented expressly to integrate the study of technology with business, law, and design. There are now over a half-dozen masters programs on offer as well as doctoral studies.

FAQ with more information about the two campuses .

Ph.D. Program Structure

Each year, about 30-40 new Ph.D. students join the department. During the first two semesters, students become familiar with the faculty members and their areas of research by taking graduate courses, attending research seminars, and participating in research projects. By the end of the first year, each student selects a specific area and forms a committee based on the student's research interests. This “Special Committee” of three or more faculty members will guide the student through to a Ph.D. dissertation. Ph.D. students that decide to work with a faculty member based at Cornell Tech typically move to New York City after a year in Ithaca.

The Field believes that certain areas are so fundamental to Computer Science that all students should be competent in them. Ph.D. candidates are expected to demonstrate competency in four areas of computer science at the high undergraduate level: theory, programming languages, systems, and artificial intelligence.

Each student then focuses on a specific topic of research and begins a preliminary investigation of that topic. The initial results are presented during a comprehensive oral evaluation, which is administered by the members of the student's Special Committee. The objective of this examination, usually taken in the third year, is to evaluate a student's ability to undertake original research at the Ph.D. level.

The final oral examination, a public defense of the dissertation, is taken before the Special Committee.

To encourage students to explore areas other than Computer Science, the department requires that students complete an outside minor. Cornell offers almost 90 fields from which a minor can be chosen. Some students elect to minor in related fields such as Applied Mathematics, Information Science, Electrical Engineering, or Operations Research. Others use this opportunity to pursue interests as diverse as Music, Theater, Psychology, Women's Studies, Philosophy, and Finance.

The computer science Ph.D. program complies with the requirements of the Cornell Graduate School , which include requirements on residency, minimum grades, examinations, and dissertation.

The Department also administers a very small 2-year Master of Science program (with thesis). Students in this program serve as teaching assistants and receive full tuition plus a stipend for their services.

Departments

• Applied Physics
• Biomedical Engineering
• Center for Urban Science and Progress
• Chemical and Biomolecular Engineering
• Civil and Urban Engineering
• Computer Science and Engineering
• Electrical and Computer Engineering
• Finance and Risk Engineering
• Mathematics
• Mechanical and Aerospace Engineering
• Technology, Culture and Society
• Technology Management and Innovation

Degrees & Programs

• Bachelor of Science
• Master of Science
• Doctor of Philosophy
• Digital Learning
• Certificate Programs
• NYU Tandon Bridge
• Undergraduate
• Records & Registration
• Digital Learning Services
• Teaching Innovation
• Explore NYU Tandon
• Year in Review
• Strategic Plan
• Diversity & Inclusion

News & Events

• Social Media

Looking for News or Events ?

Computer Science, Ph.D.

• Request Information

We have a thriving Ph.D. program with approximately 80 full-time Ph.D. students hailing from all corners of the world. Most full-time Ph.D. students have scholarships that cover tuition and provide a monthly stipend. Admission is highly competitive. We seek creative, articulate students with undergraduate and master's degrees from top universities worldwide. Our  current research strengths  include data management and analysis, cybersecurity, computer games, visualization, web search, graphics, vision and image processing, and theoretical computer science.

This degree program offers interested students opportunities to do their research abroad, under the supervision of faculty at NYU Shanghai or  NYU Abu Dhabi .

• View the Computer Science Ph.D. program flyer
• Admissions requirements for the Ph.D. Program.
• Find out more about general  Admission Requirements .

To receive a Ph.D. in Computer Science at the NYU Tandon School of Engineering, a student must:

• satisfy a breadth course requirement, intended to ensure broad knowledge of computer science,
• satisfy a depth requirement, consisting of an oral qualifying exam presentation with a written report, to ensure the student's ability to do research,
• submit a written thesis proposal and make an oral presentation about the proposal,
• write a Ph.D. thesis that must be approved by a dissertation guidance committee and present an oral thesis defense, and
• satisfy all School of Engineering requirements for the Ph.D. degree, as described in the NYU Tandon School of Engineering bulletin, including graduate study duration, credit points, GPA, and time-to-degree requirements.

Upon entering the program, each student will be assigned an advisor who will guide them in formulating an individual study plan directing their course choice for the first two years. The department will hold an annual Ph.D. Student Assessment Meeting, in which all Ph.D. students will be formally reviewed.

Note: for pre-fall 2015 Ph.D. students, please see the pre-fall 2015 Ph.D. Curriculum.

Program Requirements

Details about Breadth and Depth Requirements, Thesis Proposal and Presentation, and Thesis Defense can be found in the NYU Bulletin.

Program Details

Each incoming Ph.D. student will be assigned to a research advisor, or to an interim advisor, who will provide academic advising until the student has a research advisor. The advisor will meet with the student when the student enters the program to guide the student in formulating an Individual Study Plan. The purpose of the plan is to guide the student’s course choice for the first two years in the program and to ensure that the student meets the breadth requirements. The plan may also specify additional courses to be taken by the student in order to acquire necessary background and expertise. Subsequent changes to the plan must be approved by the advisor.

Sample Plan of Study

In order to obtain a Ph.D. degree, a student must complete a minimum of 75 credits of graduate work beyond the BS degree, including at least 21 credits of dissertation. A Master of Science in Computer Science may be transferred as 30 credits without taking individual courses into consideration. Other graduate coursework in Computer Science may be transferred on a course-by-course basis. Graduate coursework in areas other than Computer Science can be transferred on a course-by-course basis with approval of the Ph.D. Committee (PHDC). The School of Engineering places some limits on the number and types of transfer credits that are available. Applications for transfer credits must be submitted for consideration before the end of the first semester of matriculation. 

All Ph.D. students will be formally reviewed each year in a Ph.D. Student Assessment Meeting. The review is conducted by the entire CSE faculty and includes at least the following items (in no particular order):

• All courses taken, grades received, and GPAs.
• Research productivity: publications, talks, software, systems, etc.
• Faculty input, especially from advisors and committee members.
• Student’s own input.
• Cumulative history of the student's progress.

As a result of the review, each student will be placed in one of the following two categories, by vote of the faculty:

• In Good Standing: The student has performed well in the previous semester and may continue in the Ph.D. program for one more year, assuming satisfactory academic progress is maintained.
• Not in Good Standing: The student has not performed sufficiently well in the previous year. The consequences of not being in good standing will vary, and may include being placed on probation, losing RA/GA/TA funding, or not being allowed to continue in the Ph.D. program.

Following the review, students will receive formal letters which will inform them of their standing. The letters may also make specific recommendations to the student as to what will be expected of them in the following year. A copy of each student’s letter will be placed in the student’s file.

Quick Links

• Graduate Admissions
• Frequently Asked Questions
• Pre-Fall 2015 Ph.D. Curriculum

Program Admissions Chair

Justin Cappos

Program director.

Rachel Greenstadt

Periwinkle Doerfler

Nektarios Tsoutsos

• Research & Faculty
• Offices & Services
• Information for:
• Faculty & Staff
• News & Events
• Contact & Visit
• About the Department
• Message from the Chair
• Computer Science Major (BS/BA)
• Computer Science Minor
• Data Science and Engineering Minor
• Combined BS (or BA)/MS Degree Program
• Intro Courses
• Special Programs & Opportunities
• Student Groups & Organizations
• Undergraduate Programs
• Undergraduate Research
• Senior Thesis
• Peer Mentors
• Curriculum & Requirements
• MS in Computer Science
• PhD in Computer Science
• Admissions FAQ
• Financial Aid
• Graduate Programs
• Courses Collapse Courses Submenu
• Research Overview
• Research Areas
• Systems and Networking
• Security and Privacy
• Programming Languages
• Artificial Intelligence
• Human-Computer Interaction
• Vision and Graphics
• Groups & Labs
• Affiliated Centers & Institutes
• Industry Partnerships
• Adobe Research Partnership
• Center for Advancing Safety of Machine Intelligence
• Submit a Tech Report
• Tech Reports
• Tenure-Track Faculty
• Faculty of Instruction
• Affiliated Faculty
• Adjunct Faculty
• Postdoctoral Fellows
• PhD Students
• Outgoing PhDs and Postdocs
• Visiting Scholars
• News Archive
• Weekly Bulletin
• Monthly Student Newsletter
• All Public Events
• Seminars, Workshops, & Talks
• Distinguished Lecture Series
• CS Colloquium Series
• CS + X Events
• Tech Talk Series
• Honors & Awards
• External Faculty Awards
• University Awards
• Department Awards
• Student Resources
• Undergraduate Student Resources
• MS Student Resources
• PhD Student Resources
• Student Organization Resources
• Faculty Resources
• Postdoc Resources
• Staff Resources
• Purchasing, Procurement and Vendor Payment
• Expense Reimbursements
• Department Operations and Facilities
• Initiatives
• Student Groups
• CS Faculty Diversity Committee
• Broadening Participation in Computing (BPC) Plan
• Northwestern Engineering

Academics   /   Graduate PhD in Computer Science

The doctor of philosophy in computer science program at Northwestern University primarily prepares students to become expert independent researchers. PhD students conduct original transformational research in extant and emerging computer science topics. Students work alongside top researchers to advance the core CS fields from Theory to AI and Systems and Networking . In addition, PhD students have the opportunity to collaborate with CS+X faculty who are jointly appointed between CS and disciplines including business, law, economics, journalism, and medicine.

Joining a Track

Doctor of philosophy in computer science students follow the course requirements, qualifying exam structure, and thesis process specific to one of five tracks :

• Artificial Intelligence and Machine Learning
• Computer Engineering

Within each track, students explore many areas of interest, including programming languages , security and privacy and human-computer interaction .

Learn more about computer science research areas

Curriculum and Requirements

The focus of the CS PhD program is learning how to do research by doing research, and students are expected to spend at least 50% of their time on research. Students complete ten graduate curriculum requirements (including COMP_SCI 496: Introduction to Graduate Studies in Computer Science ), and additional course selection is tailored based on individual experience, research track, and interests. Students must also successfully complete a qualifying exam to be admitted to candidacy.

CS PhD Manual Apply now

Request More Information

Download a PDF program guide about your program of interest and get in contact with our graduate admissions staff.

Request info about the PhD degree

Opportunities for PhD Students

Cognitive science certificate.

Computer science PhD students may earn a specialization in cognitive science by taking six cognitive science courses. In addition to broadening a student’s area of study and improving their resume, students attend cognitive science events and lectures, they can receive conference travel support, and they are exposed to cross-disciplinary exchanges.

The Crown Family Graduate Internship Program

PhD candidates may elect to participate in the Crown Family Graduate Internship Program. This opportunity allows the doctoral candidate to gain practical experience in industry or in national research laboratories in areas closely related to their research.

Management for Scientists and Engineers Certificate Program

The certificate program — jointly offered by The Graduate School and Kellogg School of Management — provides post-candidacy doctoral students with a basic understanding of strategy, finance, risk and uncertainty, marketing, accounting and leadership. Students are introduced to business concepts and specific frameworks for effective management relevant to both for-profit and nonprofit sectors.

Career Paths

Recent graduates of the computer science PhD program are pursuing careers in industry & research labs, academia, and startups.

• Georgia Institute of Technology
• Illinois Institute of Technology
• Northeastern
• University of Pittsburgh
• University of Rochester
• University of Washington
• Naval Research Laboratory
• Northwestern University

Industry & Research Labs

• Adobe Research
• Narrative Science
• Oak Ridge National Laboratory

More in this section

• Engineering Home
• CS Department

Related Links

• The Graduate School
• Graduate Funding
• International Office
• Graduate Housing
• Meet Our Faculty

Contact Info

Admissions Questions

Help for Current PhD Students

Director of Graduate Studies for PhD Program

What Students Are Saying

"One great benefit of Northwestern is the collaborative effort of the CS department that enabled me to work on projects involving multiple faculty, each with their own diverse set of expertise.

Northwestern maintains a great balance: you will work on leading research at a top-tier institution, and you won't get lost in the mix."

— Brian Suchy, PhD Candidate, Computer Systems

What Alumni Are Saying

"In the early stage of my PhD program, I took several courses from the Department of Economics and the Kellogg School of Management and, later, I started collaborating with researchers in those areas. The experience taught me how to have an open mind to embrace and work with people with different backgrounds."

— Yiding Feng (PhD '21), postdoctoral researcher, Microsoft Research Lab – New England

Read an alumni profile of Yiding Feng

"My work at IBM Research involves bringing together symbolic and deep learning techniques to solve problems in interpretable, effective ways, which means I must draw upon the research I did at Northwestern quite frequently."

— Maxwell Crouse (PhD '21), AI Research Scientist, IBM Research

Read an alumni profile of Maxwell Crouse

The theory group here is very warm and close-knit. Starting a PhD is daunting, and it is comforting to have a community I can lean on.

— Vaidehi Srinivas, PhD Candidate, CS Theory

Doctoral Degree in Computer Science

Carnegie Mellon's Ph.D. in Computer Science is, above all, a research degree. When the faculty award a Ph.D., they certify that the student has a broad foundation and awareness of core concepts in computer science, has advanced the field by performing significant original research and has reported that work in a scholarly fashion.

When you begin our Ph.D. program, you’ll take the Introductory Course for Doctoral Students — an intense two week program that orients you to the department, introduces you to research and education topics our faculty are interested in, helps you find a faculty advisor and familiarizes you with Carnegie Mellon’s resources. Next, you’ll gain a broad understanding of fundamental research issues in major areas of computer science through coursework and original research. Finally, you’ll write and orally defend a thesis that guarantees you understand the area well enough to advance the state of knowledge in the field.

During the first two years of the program, you’ll gain the foundation of knowledge that will allow you to become an expert researcher in computer science, primarily by

Mastering a body of graduate material, achieved by passing 96 university units worth of graduate courses (equivalent to eight full-time courses).

Learning how to organize and begin to carry out original research, achieved by participating in directed research.

You will also serve as a teaching assistant, hone your writing and speaking skills and maintain your programming prowess. You’ll also receive periodic evaluation of your progress, and must make satisfactory progress to continue in the program.

Time Commitment:

As a Ph.D. student in computer science at CMU, you'll spend roughly five years acquiring a body of technical knowledge that includes a familiarity with the breadth of the field, as well as a deep understanding of your research area. From your second month in the program, you'll work closely with your faculty advisor, who is charged with guiding your education and monitoring your progress through the program. You'll take courses, teach and perform directed research — all to ensure that you leave Carnegie Mellon as an expert in your field. For a complete breakdown of our program requirements, read our Ph.D. Handbook .

Financial Information:

The Computer Science Department offers all Ph.D. students full financial support while they are in good academic standing in their respective programs. To learn more about Ph.D. funding, visit the SCS  Doctoral Programs  webpage.

Graduate Tuition: https://www.cmu.edu/sfs/tuition/graduate/scs.html

Student Fees: https://www.cmu.edu/sfs/tuition/fees/index.html

Carnegie Mellon Graduate Student Financial Aid: https://www.cmu.edu/sfs/financial-aid/graduate/index.html

• Bachelor's Programs
• Master's Programs
• Ph.D. in Computer Science
• Ph.D. in ACO
• Doctoral - How to Apply
• Degrees Conferred
• Other SCS Doctoral Programs
• Student Resources

Ph.D. in Computer Science

Ph.d. program requirements.

The PhD degree requires 72 graduate-level credits, including:

• no 5000-level CS courses
• these credits traditionally cannot be transferred in, you must actually take at least 6 credits of coursework at UVA to get a UVA PhD
• CS 8897 and CS 9897 (Graduate Teaching Instruction) cannot be used to satisfy this 24-credit requirement (but see below)
• at least 12 credits in any combination of CS 8897 and CS 9897 (Graduate Teaching Instruction), corresponding to two semesters as a full-time, 20 hour per week TA (see Chapter 3.2)
• Completion of the Qualifying Examination (see Chapter 5)
• Completion of the PhD Proposal (see Chapter 6.3)
• Completion of the Oral Defense of the written Dissertation (see Chapter 6.4)
• Finally, complete the “ Graduate Student Leave Request ” form (see Section 2.5) to leave the program.

These requirements have significant overlap with the MCS and MS degree requirements; many students choose to earn one of those Master’s degrees as part of their PhD studies.

Application Requirements

Computer science background requirements.

The Department of Computer Science does not require that applicants hold a bachelor's degree in Computer Science. However, applicants are expected to have a strong background in Computer Science. A suitable background would include courses in the following core areas:

• Data Structures
• Discrete Mathematics
• Assembly Language and Computer Organization
• Programming in a procedural language such as C, C#, C++, or Java.

Applicants are also expected to have taken several (but not necessarily all) courses in specialized areas:

• Operating Systems
• Programming Languages
• Artificial Intelligence
• Computer Networks
• Automata and Formal Languages
• Software Engineering

A year of college-level Calculus is also required. In general, experience gained working is not considered equivalent to successful completion of the courses listed above.

Grade Point Average

There is no minimum GPA required for admission. However, most applicants who are offered admission to our program have a GPA of at least 3.3 (out of 4.0). The grades in Computer Science, mathematics and related courses are more important than the overall GPA.

GRE scores are optional. 

Letters of Reference

If possible, letters of references should be written by faculty at a university previously attended. Letters of reference from Computer Science faculty are preferred, but references from employers are welcome. References should pay particular attention to academic achievements and evidence of independent, creative problem solving.

TOEFL/IELTS Scores

• If you are a permanent resident of the U.S., TOEFL is not required
• If you received a 4-year degree at an English-speaking institution (whether or not the institution is in the U.S.), TOEFL/IELTS is not required.
• If you received a 4-year degree at a non -English-speaking institution and a Master's degree from an English-speaking institution, TOEFL/IELTS is required. 
• Note that if you have a solid command of written and spoken English, TOEFL/IELTS waivers are possible! Contact via email,  [email protected] , explaining why you believe TOEFL/IELTS can be waived (include evidence such as verification of duties as a Teaching Assistant that required significant interactions in English, copies of expired TOEFL/IELTS scores, presentations at conferences in English, etc.). 

It is unusual that we offer admission to an applicant with an overall TOEFL score below 90 / IELTS below 6.5. Scores can be sent electronically to UVa at institution code B875. Some students with lower scores may be required to complete the UVA Summer English for Academic Purposes Program prior to admission.

Application Evaluation

Applications are evaluated based on the following factors:

• Background in Computer Science (including project work)
• Grade Point Average (GPA)
• Graduate Record Examination (GRE)
• Letters of reference
• Personal statement
• TOEFL/IELTS scores

Applications are evaluated in their entirety. A weakness in one factor might be mitigated by strength in another.

Financial Aid / Tuition 

Occasionally, the school of Engineering offers Master Fellowships. More information can be found on the Engineering Cost Aid webpage: https://engineering.virginia.edu/future-grads/graduate-admissions/cost-aid , and you can learn more about UVA Fellowships here: https://citizenscholars.virginia.edu/fellowships  

PhD students are usually admitted with a financial aid package in the form of a First-Year Research Assistantship that allows students to explore research with various faculty members and find their best match. It is expected that students will join a research group by the end of their first year and then be supported as a Research Assistant (RA). This financial aid package includes a competitive stipend, tuition, fees, and health insurance coverage. Details of this award are given at the time of your notification of acceptance into the Computer Science PhD program.  

You are encouraged to apply to outside sources for fellowships or you can apply for federal assistance by filling out a Free Application for Federal Student Aid .

The UVA Tuition and Fees page includes the costs per academic year by school. 

CS Admissions Frequently Asked Questions (FAQs)

How do i apply.

Please visit this Web page to apply.

When is the application deadline?

See details in the section above (Admissions).

How much does it cost to apply? Can this fee be waived?

Visit this UVA Engineering FAQ page for details on the cost to apply, and learn if your fee can be waived.

Is the TOEFL/IELTS required?

International students must have an outstanding command of the English language in order to enroll at the University of Virginia. The TOEFL/IELTS exam is required of all applicants if the language first learned and spoken in the home is not English, and they are not permanent residents. However, TOEFL/IELTS is not required if the applicant has received a 4-year degree at an English-speaking institution (whether or not the institution is in the U.S.). (If the applicant has a 4-year degree from a non-English-speaking institution and a Master's degree from an English-speaking institution, TOEFL/IELTS is still required.) It is unusual that we offer admission to an applicant with an overall TOEFL score below 90 / IELTS below 6.5. 

I scored less than 22 on the Speaking section of TOEFL. Can I still apply?

We review all applications thoroughly, along a number of dimensions. It is unusual that we offer admission to an applicant with an overall TOEFL score below 90/ IELTS score of 6.5.

Where do I send my GRE and/or TOEFL/IELTS scores?

The Institution code for School of Engineering and Applied Science of the University of Virginia for the GRE is 5820. The code for TOEFL is  B875. There is not a specific code for the Department of Computer Science.

I'm taking TOEFL/IELTS or GRE after your deadline (Dec 15). If I apply will these scores make it into my application and be seen by the admissions committee?

We will start evaluating applications soon after the Dec 15 deadline. Applicants should submit the most complete application they can, based on the information they have at the time (e.g., current test scores, even if new test scores are anticipated).Those applications that are complete will be considered first. We will continue to evaluate applications into early next year, until we have completed our offers. As we are reviewing applications, we will certainly consider updated scores as the arrive at the University of Virginia. There is no need to email us to tell us that new scores are being sent.

Should I mail or should I upload my materials with my application?

We strongly discourage applicants from mailing in any items that can be uploaded to avoid delays in your application review, and we ask that you not send duplicate copies of previously uploaded documents. If you still need to mail documents to our office, please send them to: For US Postal: Graduate School of Engineering and Applied Science Admissions P.O. Box 401103 Charlottesville, VA 22904 For UPS/FEDEX:      Graduate School of Engineering and Applied Science Admissions      1001 Emmet Street North      Room 209B Carruthers Hall      Charlottesville, VA 22903

I’ve submitted my application and all supporting materials. Why does my application status still show as incomplete?

We will fully review your application with unofficial test scores and unofficial transcripts. Your application will only show as "complete" when your application has been submitted, your official scores and transcripts have been received and all three letters of recommendations have been received. An application is complete for review with unofficial transcripts and self-reported scores, though the checklist will still show incomplete. Please note that all official transcripts are received in our main admissions office and scanned or entered into our system manually. If you feel that your materials should have been received by now, but are NOT showing up when you login to your account, please note that the Graduate Admissions Office processes a very large number of applications and it may take longer than expected for your documents/information to appear online (in your account). It is very likely that your materials have been received, but have not been loaded into our application system yet.

If I email you my information (e.g., GPA, GRE scores, etc.) before I apply, can you tell me the chance of being accepted?

The graduate admissions committee considers many factors in an application, including more than just GPA and test scores. In particular, letters of reference and your personal statement are extremely important. Therefore, we are unfortunately unable to provide any information before the committee considers your full application.

I still have other questions. Is there anyone available to help me?

Yes! For program/degree specific questions, please send an email to [email protected]. For application support and specific questions regarding the application process, please contact: Central Graduate Admissions [email protected] 434-243-0209

The information contained on this website is for informational purposes only.  The Undergraduate Record and Graduate Record represent the official repository for academic program requirements. These publications may be found here .

PhD in Computer Science

The PhD in Computer Science program provides students with the advanced coursework and groundbreaking research opportunities they need to contribute at the forefront of the world’s fastest-growing fields. Forging knowledge in 15 core areas like artificial intelligence, data science, programming languages, and human-centered computing, you’ll gain significant expertise in conducting and presenting the results of your research. Ultimately, you’ll produce and defend original work that contributes to critical discourse in your chosen area.

• Explore plan of study
• View program requirements
• How to apply
• Request info

Khoury College doctorate students gain deep knowledge and invaluable experience—preparing you for a research career in academia or industry.

Khoury Computer Science PhD graduates have found prestigious positions across industry and academia.

Tenure-track faculty:

• University of Michigan, Ann Arbor
• University of British Columbia (UBC)
• Indiana University
• University of Maryland
• University College London
• NC State University
• UMass Boston
• City University of Hong Kong

Postdoc research scientists:

• University of Paris
• Virginia Tech
• Microsoft Research
• GE Global Research

Senior software engineers and industry leaders:

Students graduating with a PhD in Computer Science will:

• Gain a broad understanding of computer science fundamentals, spanning a substantial portion of the following core areas: artificial intelligence and data science, human-centered computing, software, systems, and theory
• Gain significant expertise in at least one research area in computer science
• Produce and defend original research in an area of computer science
• Be able to communicate research results effectively in both oral and written forms

Our flagship campus in Boston is just minutes away from esteemed universities, exciting start-ups, and leaders in tech, finance, health care, and more.

FEATURED RESEARCH

August 1, 2024

Khoury Graduate Admissions Team

• Financial support

January 1, 1066

January 1, 1492

Khoury Align Admissions Team

• How to Apply
• Cost & Financial Aid

Khoury Social

Contact Khoury

I'm seeking information for

Ph.D. Program

The Allen School provides every student accepted to our Ph.D. program with full financial support in the form of teaching and research assistantships or fellowships, from program inception to degree. Students earn an integrated Master’s Degree on their path to the Ph.D. Key features of our program include:

• Comprehensive, high-quality graduate computer science curriculum.
• A vibrant academic and social community.
• Welcoming and inclusive environment for international students, women, and other underrepresented groups.
• Robust schedule of colloquia and lectures on current topics in research and technology.
• Leading-edge interdisciplinary research opportunities, on and off campus.

Our students benefit from many collaborations and relationships that we have developed across the campus and in the region. In addition to being the headquarters of established technology leaders such as Microsoft and Amazon, Seattle is also home to an extensive (and ever-growing) list of engineering centers established by major industry players from outside the Pacific Northwest.

Admission to the Allen School’s Ph.D. program is competitive. Each year, we receive applications from approximately 2,500 prospective graduate students from around the globe for 50 - 60 positions. We accept applications once a year, for entrance in the following autumn quarter. Our application process opens on September 1, and all application materials are due December 15, or the next following business day, if the 15th falls on a weekend. The Allen School hosts its annual Grad Visit Days in March for applicants who have received an offer of admission. This event provides an opportunity for applicants to meet with faculty, get to know their prospective colleagues, and experience the Seattle area’s quality of life.

The Ph.D. Process

The Allen School's Ph.D. process consists of three components: coursework, research, and thesis preparation. At the beginning of the program, students will take graduate-level courses in an array of topics spanning theory, systems, programming, and applications. They will also develop and refine their research skills working with their faculty advisor and other collaborators. These skills include information analysis and synthesis as well as written and verbal presentation capabilities. Student progress is measured at multiple steps throughout the program: the Qualifying Evaluation (a.k.a. “quals”), the General Exam, and the Candidacy of Philosophy, leading to the preparation and defense of their dissertation to obtain their Doctor of Philosophy degree.

Course Guide

Students are required to complete approximately 90 credits on their way to obtaining a Ph.D. degree in Computer Science & Engineering from the Allen School, 60 of which must be earned at the University of Washington. Explore our online course guide to peruse available courses, teaching schedules, internship credit, and specialized degree tracks available to Ph.D. students.

Student Handbook

Visit our online student handbook for essential information and advice about being a Ph.D. student in the Allen School, from available fellowships and travel grants, to navigating the annual review of progress, to mentoring undergraduate researchers. This section also contains practical information such as allocation of office space and obtaining health insurance, as well as the forms students will need to complete at various points throughout the program.

The Allen School's graduate advising team is here to guide prospective and current students as they navigate the application and registration process and help tailor the Allen School experience to their education and career goals.

College of Computing

Ph.D. in Computer Science

All students in the program receive the same degree regardless of their interest area, specialization, research focus or school affiliation. New students are affiliated with the school in which their advisor resides, but none of the schools impose any special requirements compared to another.

As a research-oriented degree, the Ph.D. in Computer Science prepares exceptional students for careers at the cutting edge of academia, industry and government. Students are expected to demonstrate excellence in both defining and executing a substantial research project that forms a novel contribution to the state of the art in computing. With a highly individualized program of study, the degree provides students with depth in their chosen research area coupled with a rigorous breadth of knowledge across the discipline.

First granting the doctoral degree in 1969 (as a Ph.D. in Information and Computer Science), the College of Computing represents a continuation of one of the earliest and most well-established graduate Computing institutions in the United States, and in the world. This stature is reflected in our national and international rankings and, most importantly, in the quality of the students who have graduated from our program.

The CS Ph.D. Structure

The coursework component of the Computer Science Ph.D. consists of an introductory course on graduate studies (CS 7001), along with the separate breadth and minor requirements.

The breadth requirement is intended to give students a broad competency across the discipline of computing through coursework in a range of the College's different research areas. This requirement is satisfied by taking five classes from across the College's different research areas and must include a Programming Proficiency course and a Theory course.

The minor is a 9-hour sequence of courses from outside the College that constitutes a coherent program of study and is determined by the student and advisor. The minor builds non-Computing expertise in an area related to the student's core research area.

As students progress, they must select a primary area of research and pass a qualifier (comprehensive exam) in that area to demonstrate mastery of the field in their chosen area, and readiness to do research.

While coursework plays an important role in the Ph.D., by far the most important component of the degree is the student's individual dissertation research project. This project should contribute to new knowledge in the field of computing, and should demonstrate the student's proficiency in defining and executing a compelling research agenda.

The dissertation research plan is formalized in a written proposal followed by an oral presentation. When a student passes his or her proposal, the student is admitted to candidacy and proceeds with the dissertation research, which is completed with the successful defense and submission of the approved doctoral dissertation.

Program of Study

Want to know more details about the program of study for the Ph.D. in CS? Find out about breadth component areas and courses, minors, qualifying exams, and more on the Ph.D. CS - Program of Study page.

Explore the Program of Study for the Ph.D. in CS

Computer Science Research

The breadth of the College's research endeavors makes our doctorate degree in computer science unique: the research specializations in the College span what is typically found in a "traditional" CS department, along with elements found in EECS, robotics, or information schools in other universities. This diversity allows students to formulate a unique individual program of study all within the CS degree, which may be impossible at other universities.

Learn more about our Areas of Research

Admissions Requirements and Applications

If this kind of work interests you and fits with your career aspirations, why not go ahead and apply?

Need more information about our admissions requirements? Find an overview of these requirements on our Ph.D. CS - Admissions Requirements page.

Ph.D. CS - Admissions Requirements

Current Ph.D. in CS Student Information

If you are a current student in our Ph.D. in Computer Science program, you can find information on your qualifying exams on our website. If you still cannot find the information you are looking for, please reach out to your assigned program advisor. 

Ph.D. CS - Qualifier Exam Information

CS Ph.D. Student Handbook

Older handbook:

2022  CS Ph.D. Student Handbook  

2021 CS Ph.D. Student Handbook

From the Catalog:

CS PhD Course Guidelines

The following program guidelines (a.k.a model pogram) serve as a starting point for a discussion with the faculty about areas of interest.   This description of the Computer Science PhD course guidelines augments the school-wide  PhD course requirements .   Students should make themselves familiar with both.

Course Guidelines for Ph.D. Students in Computer Science

We expect students to obtain broad knowledge of computer science by taking graduate level courses in a variety of sub-areas in computer science, such as systems, networking, databases, algorithms, complexity, hardware, human-computer interaction, graphics, or programming languages.

Within our school, CS courses are roughly organized according to sub-area by their middle digit, so we expect students to take courses in a minimum of three distinct sub-areas, one of which should be theory (denoted by the middle digit of 2, or CS 231). Theory is specifically required as we expect all students to obtain some background in the mathematical foundations that underlie computer science. The intention is not only to give breadth to students, but to ensure cross-fertilization across different sub-disciplines in Computer Science.

Just as we expect all students obtaining a Ph.D. to have experience with the theoretical foundations of computer science, we expect all students to have some knowledge of how to build large software or hardware systems , on the order of thousands of lines of code, or the equivalent complexity in hardware. That experience may be evidenced by coursework or by a project submitted to the CHD for examination. In almost all cases a course numbered CS 26x or CS 24x will satisfy the requirement (exceptions will be noted in the course description on my.harvard). Students may also petition to use CS 161 for this requirement.   For projects in other courses, research projects, or projects done in internships the student is expected to write a note explaining the project, include a link to any relevant artifacts or outcomes, describe the student's individual contribution, and where appropriate obtain a note from their advisor, their class instructor, or their supervisors confirming their contributions.  The project must include learning about systems concepts, and not just writing many lines of code.   Students hoping to invoke the non-CS24x/26x/161 option must consult with  Prof. Mickens ,  Prof, Kung,  or  Prof. Idreos  well in advance of submitting their Program Plan to the CHD.  

Computer science is an applied science, with connections to many fields. Learning about and connecting computer science to other fields is a key part of an advanced education in computer science. These connections may introduce relevant background, or they may provide an outlet for developing new applications.

For example, mathematics courses may be appropriate for someone working in theory, linguistics courses may be appropriate for someone working in computational linguistics, economics courses may be appropriate for those working in algorithmic economics, electrical engineering courses may be appropriate for those working in circuit design, and design courses may be appropriate for someone working in user interfaces.

Requirements

The Graduate School of Arts & Sciences (GSAS) requires all Ph.D. students to complete 16 half-courses (“courses”, i.e., for 4 units of credit) to complete their degree. Of those 16 courses, a Ph.D. in Computer Science requires 10 letter-graded courses. (The remaining 6 courses are often 300-level research courses or other undergraduate or graduate coursework beyond the 10 required courses.)

The requirements for the 10 letter-graded courses are as follows:

• Of the 7 technical courses, at least 3 must be 200-level Computer Science courses, with 3 different middle digits (from the set 2,3,4,5,6,7,8), and with one of these three courses either having a middle digit of 2 or being CS 231 (i.e., a “theory” course).   Note that CS courses with a middle digit of 0 are valid technical courses, but do not contribute to the breadth requirement.
• At least 5 of the 8 disciplinary courses must be SEAS or SEAS-equivalent 200-level courses. A “SEAS equivalent” course is a course taught by a SEAS faculty member in another FAS department. 
• For any MIT course taken, the student must provide justification why the MIT course is necessary (i.e. SEAS does not offer the topic, the SEAS course has not been offered in recent years, etc.). MIT courses do not count as part of the 5 200-level SEAS/SEAS-equivalent courses. 
• 2 of the 10 courses must constitute an external minor (referred to as "breadth" courses in the SEAS “ Policies of the Committee on Higher Degrees [CHD] ”) in an area outside of computer science. These courses should be clearly related; generally, this will mean the two courses are in the same discipline, although this is not mandatory. These courses must be distinct from the 8 disciplinary courses referenced above.
• Students must demonstrate practical competence by building a large software or hardware system during the course of their graduate studies. This requirement will generally be met through a class project, but it can also be met through work done in the course of a summer internship, or in the course of research.
• In particular, for Computer Science graduate degrees, Applied Computation courses may be counted as 100-level courses, not 200-level courses.
• Up to 2 of the 10 courses can be 299r courses, but only 1 of the up to 2 allowed 299r courses can count toward the 8 disciplinary courses. 299r courses do not count toward the 5 200-level SEAS/SEAS-equivalent courses. If two 299r’s are taken, they can be with the same faculty but the topics must be sufficiently different.
• A maximum of 3 graduate-level transfer classes are allowed to count towards the 10 course requirement.
• All CS Ph.D. program plans must adhere to the SEAS-wide Ph.D. requirements, which are stated in the SEAS Policies of the Committee on Higher Degrees (CHD) . These SEAS-wide requirements are included in the items listed above, though students are encouraged to read the CHD document if there are questions, as the CHD document provides further explanation/detail on several of the items above.
• All program plans must be approved by the CHD. Exceptions to any of these requirements require a detailed written explanation of the reasoning for the exception from the student and the student’s research advisor. Exceptions can only be approved by the CHD, and generally exceptions will only be given for unusual circumstances specific to the student’s research program.

Requirement Notes

• Courses below the 100-level are not suitable for graduate credit.
• For students who were required to take it, CS 2091/2092 (formerly CS 290a/b or 290hfa/hfb may be included as one of the 10 courses but it does not count toward the 200-level CS or SEAS/SEAS-equivalent course requirements nor toward the SM en route to the PhD.

Your program plan  must always comply  with both our school's General Requirements, in addition to complying with the specific requirements for Computer Science. All program plans must be approved by the Committee on Higher Degrees [CHD]. Exceptions to the requirements can only be approved by the CHD, and generally will only be given for unusual circumstances specific to the student’s research program

In Computer Science

• First-Year Exploration
• Concentration Information
• Secondary Field
• Senior Thesis
• AB/SM Information
• Student Organizations
• How to Apply
• PhD Timeline
• PhD Course Requirements
• Qualifying Exam
• Committee Meetings (Review Days)
• Committee on Higher Degrees
• Research Interest Comparison
• Collaborations
• Cross-Harvard Engagement
• Lecture Series
• Clubs & Organizations
• Centers & Initiatives
• Alumni Stories

Computer Science & Engineering

Doctoral Programs in Computer Science and Engineering

Updated January 2023

PhD Program Overview

The following requirements are for students who entered the program starting Fall 2018 or later. If you entered Doctoral Program  prior to Fall 2018  see our  Former Curriculum Requirements .

CSE offers Doctor of Philosophy degrees in Computer Science and in Computer Engineering, providing a research-oriented education in preparation for a research, industrial, or entrepreneurial career. These programs explore both the fundamental aspects and application of computation, spanning theory, software, hardware, and applications.

The 37-unit coursework requirement is intended to ensure that students are exposed to (1) fundamental concepts and tools, (2) advanced, up-to-date views in topics outside their area (the breadth requirement), and (3) a deep, up-to-date view of their research area (the elective requirement). Doctoral students are expected to complete the breadth and elective requirements within the first three years of the program. All required coursework must be taken for a letter grade, with the exception of CSE 292 (Faculty Research Seminar), which is only offered S/U.

To access the CSE PhD Program Course Planner worksheet:   click here

Units obtained from a single course cannot count towards both the breadth and the elective requirements; they may only be applied towards one or the other. Doctoral students who have taken similar courses elsewhere may petition for a waiver of the required courses or for substitution by alternative courses.

The breadth requirement ensures that doctoral students share knowledge of fundamental concepts and tools from across broad areas of computer science and computer engineering. Each doctoral student must take each of these courses for a letter grade and maintain an overall breadth course GPA of 3.3 (except for CSE 292, for which a letter grade is not assigned). A student will typically complete all breadth courses within the first two years of graduate study.  Breadth courses are categorized into ten areas and are listed here alphabetically:

• Artificial Intelligence 
• Bioinformatics
• Computer Engineering
• Computer Systems & Security
• Database Systems
• Graphics & Vision
• Human-computer Interaction 
• Programming Languages, Compilers, and Software Engineering
• Theoretical Computer Science

To fulfill the breadth requirement, students will select four out of the ten areas and take a single course from each of these four areas.

For courses approved to fulfill the breadth requirement, please see the CSE Graduate Course Structure for PhD Students.

Additionally, students are required to take CSE 292, a 1-unit Faculty Researcher Seminar, where CSE faculty present one-hour seminars of their current research work in their areas of interest.  This course is only taught in Fall quarters and offered for S/U grade only.

The elective requirement ensures that doctoral students acquire some depth of knowledge in a general research area early in their career, but it also does not preclude them from pursuing a breadth of topics, if it serves their research interests. The elective requirement is designed to be flexible and nimble enough to respond to the rapidly and constantly evolving dynamic disciplines of computer science and computer engineering. 

The elective requirement is also designed with heavy faculty mentorship in mind.  Students will consult with their faculty advisors to develop an academic plan that will include four courses from the aforementioned four separate breadth areas and five elective courses that may be selected from an approved set of courses featured in the  CSE Graduate Course Structure for PhD Students.

Units obtained in the CSE 209 series, 229 series, 239 series, 249 series, 259 series, 269 series, 279 series, 289 series, 219, 290, 292, 293, 294, 298, 299, 500, and 599 do not count toward the elective requirement.

The research exam in the first milestone in the Ph.D. program.  It has three goals:

• Depth . The research exam verifies the student's ability to identify challenges and open problems in a focused area.  The exam should teach students how to navigate, acquire depth of knowledge, and perform critical analysis in a given research area; the exam should verify such abilities.
• Communication . The research exam will verify the student's ability to communicate past and proposed research, orally and in writing.
• Provide diverse feedback . The research exam provides the student with feedback on their research synthesis, analysis, and communication skills from CSE faculty beyond their advisor and outside their immediate research area.

As part of the exam, the student prepares and makes a presentation to their research exam committee.  The presentation can present results of their research and must also place that work in the context of related work in the field.

The exam committee comprises three faculty members (not including the student’s advisor), and the committee evaluates the student based on the goals above.

Student should complete the exam before the end of their second year of study.

Teaching is an important part of a doctoral student’s training. All students enrolled in the doctoral program must have one quarter of training as a teaching assistant. This is a formal degree requirement and must be completed before the student is permitted to graduate. The requirement is met by serving as a 50 percent teaching assistant and taking CSE 500 (Teaching Assistantship). CSE 599 (Teaching Methods in Computer Science) examines theoretical and practical communication and teaching techniques particularly appropriate to computer science, and students usually take it prior to or concurrent with the teaching assistantship.

The qualifying examination is a requirement for advancement to candidacy. Prior to taking the qualifying examination, a student must have satisfied the departmental course and research exam requirements and must have been accepted by a CSE faculty member as a doctoral thesis candidate. All doctoral students are expected to advance to candidacy by the end of their third year, and advancement is mandatory by the end of the fourth year. The examination is administered by a doctoral committee appointed by the dean of the Graduate Division and consists of faculty from CSE and other departments. More information on the composition of the committee can be obtained from the CSE graduate office. The examination is taken after the student and his or her adviser have identified a topic for the dissertation and an initial demonstration of feasible progress has been made. The candidate is expected to describe his or her accomplishments to date as well as future work.

The dissertation defense is the final doctoral examination. A candidate for the doctoral degree is expected to write a dissertation and defend it in an oral examination conducted by the doctoral committee. 

Students must be advanced to candidacy by the end of four years. Total university support cannot exceed seven years. Total registered time at UC San Diego cannot exceed eight years.

PhD students may obtain an MS Degree along the way or a terminal MS degree by completing the PhD coursework requirements (see details in the section “Doctoral Degree Program”); AND completing four units of CSE 299/298/293 OR an additional 4-unit, letter-graded, approved course from the CSE Graduate Course Structure; AND passing the PhD Research Exam.  Please note that completion of CSE 292 is not required for PhD students to earn the MS along the way or a terminal MS.

Financial support is available to qualified graduate students in the form of fellowships, loans, and assistantships. For questions about financial support, please see our website: http://cse.ucsd.edu/graduate/financial-opportunities .

Jump to navigation

• UTCS Direct

PhD Program

The PhD is a research degree. Our PhD students also take courses, which give them the foundation on which to build their research programs. However, the overriding goal of the PhD program is to show students how to conduct outstanding research. We expect all our PhD students to become involved in research within their first semester (see Research Immersion below) and continue their involvement throughout their time at UT. To understand how our PhD students are involved in our research activities, browse our research web pages .

As a consequence of early immersion in research, our PhD students are often already recognized in the wider research community well before they graduate. They regularly travel to conferences, present papers, and often receive best paper awards.

Interested in applying? Visit our Prospective Students page for information about applying to our program.

Most PhD students receive financial support from the department. Please see the financial information page for more information about this.

• Undergraduate Office
• Graduate Office
• Office of External Affairs
• Mission Statement
• Emergency Information
• Site Policies
• Web Accessibility Policy
• Web Privacy Policy

Online Doctorate in Computer Science

Online Computer Science Ph.D.: An Overview

Top schools with online computer science ph.d. programs, jobs for computer science ph.d. holders, prerequisites for an online computer science ph.d., online coursework.

• Data visualization.
• Machine learning.
• Database management systems.
• Advanced computer architecture.
• Information quality theory.

How long does a Ph.D. in computer science take to complete?

Cost and return on investment (roi), how much does a computer science ph.d. cost, how to estimate the return on investment (roi) of your degree, example courses.

• Artificial intelligence
• Algorithm design
• Analytics for big data
• Futuring and innovation
• Cybersecurity management

Job Outlook and Salaries for Graduates

Pay for online ph.d. in computer science degrees.

The PhD in CSE

The doctoral degree, i.e. the Ph.D., is primarily intended for students desiring a career in research and/or collegiate teaching.  The focus is on advanced CSE topics, on learning to perform research and to write research papers, and on making fundamental new contributions to a CSE topic. Students take advanced course work and write a  doctoral dissertation , also called a  thesis .

Program overview

Students newly admitted to the doctoral program are classified as  precandidates . Upon entering a doctoral program, there is a Ph.D. qualifying process, normally completed during the first two years. After all requirements except the dissertation are completed, students become  candidates . Students entering a CSE doctoral program with a bachelor’s degree typically become candidates in the third year and are strongly encouraged to complete the degree within five years. Such students ordinarily complete the requirements for a master’s degree along the way and receive this degree in addition to the Ph.D. A masters thesis is optional. Students who enter a CSE doctoral program with a master’s in the field of their program typically become candidates in their second year and are strongly encouraged to complete the degree within four years. Such students are not ordinarily eligible to receive a CSE master’s degree.

The complete doctoral requirements can be found in the  CSE Graduate Program Guide (Google Doc) .

View a list of courses approved for the different doctoral degree requirements (Google Sheet) .

Continuous enrollment

In order to encourage timely completion of the degree, University policy requires doctoral students to register every Fall and Winter term until their degree is completed, with very few exceptions. That is, doctoral students cannot take time off from their studies, or pursue the later stages of their degree without registering, except in special circumstances.

Transferring credits

A limited number of graduate credits earned elsewhere may be transferred to meet the coursework requirements for doctoral students earning a master’s degree. In addition, a course taken elsewhere that is equivalent to a course satisfying a degree requirement here can be used to satisfy the requirement, even if course credits are not transferred. If granted, however, such equivalency does not not reduce the total number of credit hours required for the master’s degree, unless the course is transferred.

Apply to a PhD program

This page has information about graduate program admissions .

Financial support

The CSE doctoral program admits only those students for whom financial support can be guaranteed for the anticipated duration of studies (five years for students entering with a BS, four years for students entering with an MS), assuming satisfactory progress is made.

Most commonly, this financial support consists of a fellowship, a research assistantship, or a teaching assistantship offered by the program, or a fellowship from outside the university, or a combination of these.

Additional funding information for prospective graduate students can be found here .

Graduate programs staff

Contact us with any questions about Computer Science and Engineering graduate programs.

[email protected]

Academic Programs

• CSE PhD Overview
• Dept-CSE PhD Overview
• CSE Doctoral Theses
• Program Overview and Curriculum
• For New CCSE Students
• Terms of Reference

MIT Doctoral Programs in Computational Science and Engineering

The Center for Computational Science and Engineering (CCSE) offers two doctoral programs in computational science and engineering (CSE) – one leading to a standalone PhD degree in CSE offered entirely by CCSE (CSE PhD) and the other leading to an interdisciplinary PhD degree offered jointly with participating departments in the School of Engineering and the School of Science (Dept-CSE PhD).

While both programs enable students to specialize at the doctoral level in a computation-related field via focused coursework and a thesis, they differ in essential ways. The standalone CSE PhD program is intended for students who intend to pursue research in cross-cutting methodological aspects of computational science. The resulting doctoral degree in Computational Science and Engineering is awarded by CCSE via the the Schwarzman College of Computing. In contrast, the interdisciplinary CSE PhD program is intended for students who are interested in computation in the context of a specific engineering or science discipline. For this reason, this degree is offered jointly with participating departments across the Institute; the interdisciplinary degree is awarded in a specially crafted thesis field that recognizes the student’s specialization in computation within the chosen engineering or science discipline.

For more information about CCSE’s doctoral programs, please explore the links on the left. Information about our application and admission process is available via the ‘ Admissions ‘ tab in our menu. MIT Registrar’s Office provides graduate tuition and fee rates as set by the MIT Corporation and the Graduate Admissions section of MIT’s Office of Graduate Education (OGE) website contains additional information about costs of attendance and funding .

CSStipendRankings: PhD Stipend Rankings

CSStipendRankings is a stipend-based ranking of top-paying computer science departments in US. We may implement support for other countries and you are welcomed to contribute! For a real academic ranking, please refer to CSRankings . For reviewing individual PhD advisors, please refer to PI Review .

• Stipend is the minimal amount of pre-tax allowance graciously granted by the institution to its PhD students. Currently, we support displaying (1) the stipend received by the majority of students , (2) the minimal guaranteed stipend , and (3) the stipend that students receive during the semester only . Note that some departments do not have guaranteed summer funding , and we are currently working to collect such data. For now, this data is not complete.
• Fees are annual non-reimbursible tariffs (including health insurance) reclaimed by said institution. See why health insurance is included in here. If the institution charges a CPT fee or summer enrollment fee for international students, they should also be counted here. In short, this should be the maximum possible fee that the institution charges.
• Living cost is calculated based on the MIT Living Wage Calculator for the institution's city. See why we use this calculator and its limitations in here .
• summer-gtd , indicating summer funding is guaranteed in this department.
• varies , indicating the amount of funding varies from advisor to advisor in this department.
• no-guarantee , indicating this department does not guarantee any funding at all (at least for a subset of its enrolled PhD students, where a PhD student is defined as a graduate student who is required to conduct research under an advisor to graduate and get a degree). Anyone who can prove this is welcomed and encouraged to submit an issue, and we will add this label immediately. See the reason here .
• cpt-fee , indicating international students in this department need to pay a fee for their CPT applications.
• striking , indicating this department is currently under a strike.
• , indicating the stipend is verified for the semesters, but not for the summer. This icon also serves as a hyperlink to the document used for verification, if the document is uploaded to a publicly accessible location, such as GitHub issues.
• , indicating we have a survey for this department. If you are a PhD student at this department, please click the icon to fill it.

To raise issues/comments : We believe issues and comments should be discussed and resolved publicly on GitHub for transparency. If you believe any data is inaccurate or have additional comments, please open an issue or a pull request . The maintainers will not respond to private messages sent to their personal or university accounts regarding this website.

* We have noticed discrepancies in the data reported for this university or department, and we suspect that it may not be entirely accurate. If you have access to more reliable information, we would appreciate it if you could share it with us.

This ranking is part informational and part satire, designed to democratize information on how PhD students in computer science and related areas are paid for their labor – inadequately , in most cases.

Most of the frontend code of this website is from CSRankings , and we intentionally used the same template. The code of this website can be found at https://github.com/CSStipendRankings/CSStipendRankings , and the data presented can be found as a CSV file here .

Contributing: Everyone is welcomed to submit patches or report the stipend via pull requests . Also, feel free to submit issues on GitHub . We encourage submitting datapoints through issues due to its ability to facilitate public discussion. Additionally, it provides the advantage of creating a hyperlink on the checkmark that directs to the corresponding issue. In most cases, we will respond to a submitted issue within a few days.

Frequent-Asked Questions: Please see FAQs here .

Disclaimer: CSStipendRankings is designed to highlight stipend situations across various institutions, based on user-submitted information. We try our best to verify their accuracy, but we cannot guarantee they are correct or up-to-date. Ultimately, while we hope you find this information useful, this should not be used as the primary basis for grad school decisions . We advocate users to do their own research before making life decisions.

THIS SOFTWARE AND INFORMATION IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS “AS IS” AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

CSStipendRankings is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License . The frontend (i.e., CSS and HTML) of this website is based on code licensed from CSRankings, a work at https://github.com/emeryberger/CSrankings . The copyright of CSRankings is owned by Emery Berger . The copyright of the non-CSRankings part of CSStipendRankings is owned by its contributors .

M.S. Leading to Ph.D.

This policy applies  only  to students who enter the PhD program without a Masters degree recognized by Columbia. Every MS/PhD track student (registration status ETCOMS) must apply for MS graduation in order to receive the MS degree from Columbia University and be awarded advanced standing towards the PhD.

The faculty will approve the MS degree application following successful completion of six (6)  breadth requirement courses completed in the Computer Science Department at Columbia, including all four (4) distribution courses and two (2) COMS electives [departmental requirement]. The student must have also satisfactorily completed at least six graduate lecture courses while enrolled for MS/PhD, not including imports, comp exams, or courses taken while an undergraduate at Columbia or Barnard, as well as 30 graduate points [SEAS requirement].

[Revised by full faculty vote, 11/6/13, to remove 4701 from the core.  Revised again by full faculty vote, 4/4/14, to abolish the core entirely and institute the distribution requirement.  Students enrolled in Spring 2014 or earlier may choose either four core courses or the four-course distribution requirement, plus two electives, to fulfill the MS/PhD requirements.  Students enrolled in Fall 2013 or earlier may treat 4701 as core for this purpose.]

Last updated on May 6, 2024.

Find open faculty positions here .

Computer Science at Columbia University

Upcoming events, class day graduate ceremony.

Sunday 3:00 pm

Baker Athletics Complex, 533 W 218th St, New York, NY 10034

Class Day Undergraduate Ceremony

Monday 11:45 am

CS Awards Ceremony and Celebration

Monday 1:00 pm

CSB 451 CS Auditorium

In the News

Press mentions, dean boyce's statement on amicus brief filed by president bollinger.

President Bollinger announced that Columbia University along with many other academic institutions (sixteen, including all Ivy League universities) filed an amicus brief in the U.S. District Court for the Eastern District of New York challenging the Executive Order regarding immigrants from seven designated countries and refugees. Among other things, the brief asserts that “safety and security concerns can be addressed in a manner that is consistent with the values America has always stood for, including the free flow of ideas and people across borders and the welcoming of immigrants to our universities.”

This recent action provides a moment for us to collectively reflect on our community within Columbia Engineering and the importance of our commitment to maintaining an open and welcoming community for all students, faculty, researchers and administrative staff. As a School of Engineering and Applied Science, we are fortunate to attract students and faculty from diverse backgrounds, from across the country, and from around the world. It is a great benefit to be able to gather engineers and scientists of so many different perspectives and talents – all with a commitment to learning, a focus on pushing the frontiers of knowledge and discovery, and with a passion for translating our work to impact humanity.

I am proud of our community, and wish to take this opportunity to reinforce our collective commitment to maintaining an open and collegial environment. We are fortunate to have the privilege to learn from one another, and to study, work, and live together in such a dynamic and vibrant place as Columbia.

Mary C. Boyce Dean of Engineering Morris A. and Alma Schapiro Professor

{{title}} {{fullname}}

Courses This Semester

• {{title}} ({{dept}} {{prefix}}{{course_num}}-{{section}})

University of South Florida

School of Interdisciplinary Global Studies

College of Arts and Sciences

Main Navigation

Graduate programs, phd in politics and international affairs.

The doctoral degree in politics and international affairs is an interdisciplinary program designed to prepare students to teach at the university and college levels and to conduct high-level research in the academic and nonacademic sectors. It combines a broad focus on international relations, comparative politics, American politics, and political theory with a critical understanding of institutions, rights, citizenship/identity, governance, global policy, and justice. Students work closely with faculty to frame their dissertation research and to advance their knowledge of their chosen fields of specialization. The program’s interdisciplinary approach to a variety of global issues provides a rich and open-ended opportunity to research current and past problems, movements, and transformations in politics.

We welcome your interest in our doctoral program. The department's deadline for fall admission is January 5. The School of Interdisciplinary Global Studies only admits for the fall semester. Students must apply online through the Office of Graduate Admissions. For a listing of the admission requirements, students should consult the Graduate Catalog . 

*Effective starting with the 2023-2024 admissions cycle, GRE test scores are no longer required for applications to our doctoral program in Politics and International Affairs*

*International students should review the Office of Admissions International Students website for additional information and requirements.

*International students are also encouraged to contact the Office of International Services for information on visas, international travel, etc. 

PLEASE NOTE: International students whose native language is not English and who want to be considered for a teaching assistantship must show proficiency in spoken English even if their TOEFL has been waived for admission to a graduate program. More information on the TOEFL requirement can be found under Admission Requirements in the graduate catalog.

Program Requirements

For the Doctoral Degree in Politics and International Affairs degree requirements, students should consult the Graduate Catalog. Students should adhere to the requirements within the Graduate Catalog under which they were admitted.

• Degree Requirements Beginning 2023-2024 Catalog

*Students can elect another catalog following the one they were admitted under. More information on this policy, and other policies, can be found in the Graduate Catalog.

*Students must request approval from the graduate director for any course not pre-approved and listed under the degree in the Graduate Catalog.

Additional information on program requirements:

Student can also select POS 6933/6747 Advanced Topics in Quantitative Political Analysis or another graduate course approved by the graduate director for the methods requirement. The Capstone Seminar will be conducted with doctorial students in Sociology and History and focus on dissertation proposal. 

Research Fields

The Doctorate in Politics and International Affairs specializes in the following four fields of research:

International Relations In the School of Interdisciplinary Global Studies, the International Relations (IR) faculty focuses on four areas of study: international relations theory, global political economy, international security, and human rights. We stress the importance of cutting-edge scholarship in our teaching of the graduate seminars as well as bridging the many emergent gaps in theory and practice in the various subfields that comprise International Relations, including American foreign policy, international ethics, global governance, and international law and organizations. One of our central aims is to advance innovative applications of the central theoretical perspectives (and their variant strands) in International Relations, namely, realism, liberalism, critical theory, constructivism, Marxism, international political theory, and gender. These applications involve in-depth theoretical and empirical analysis of key global issues, such as Asian security, moral accountability, the enforcement of human rights, immigration, and political and economic inequality. The International Relations faculty have published numerous books and peer-reviewed articles on these issue areas. These include monographs on the political tensions on the Korean Peninsula or North Korea’s nuclear arms buildup, the political cosmopolitan character and shifting dynamics of the International Criminal Court (ICC), hegemony and inequality in the global political economy, and China’s rapidly increasing support of intervention in African states. Together our published research emphasizes the production of critical theoretic knowledge, or the advanced methodological analysis of the contradictions and tensions informing the substantive debates in International Relations. This not only requires the particular mastery of concepts, methods, and claims but also an open-ended and historical understanding of the changing social forces shaping the behavior of states and the relations among global and local actors. It is this scholarly approach that we adopt to train our graduate students specializing in international relations, particularly as they advance their dissertation research and empirical knowledge of the global and regional contexts of problems and issues. One of the outcomes we strive for, then, is to encourage our doctoral students to develop rigorous theoretical and contextual analysis from which they can devise solutions and prescriptions to global issues.

Comparative Politics Comparative Politics in the School of Interdisciplinary Global Studies is committed to theory-driven, empirical research from an interdisciplinary perspective that is situated in a political, historical, cultural, and economic context.  The Comparative Politics faculty employ a variety of methodological approaches from both the social sciences and humanities, which utilize qualitative and quantitative research methods to study the patterns of similarities and differences. In particular, we conduct comparative and case study research to inquire into these patterns and to develop our theoretical propositions. One of our aims is to produce knowledge about the changing social, political, and legal conditions affecting the lives, development, cultural practices, and customs of underrepresented peoples. In meeting this aim, our research focuses on several themes of comparative politics, including social movements, democracy/democratization, citizenship, decolonization, genocide, hegemony, race and identity, development, legal systems and customary law, social justice, and indigenismo or the political ideology focusing on the changing relations of state and local peoples. Much of our published research draws creatively on social, critical, and political theory to advance knowledge of the laws, changing social relations, and attitudes in several countries, which includes Brazil, Ecuador, the Democratic Republic of Congo, Rwanda, Uganda, South Sudan, Ethiopia, and Iran. Our research strengths lie in the areas of race and citizenship, social movements theory, human security and law (or legal custom) in Eastern Africa, indigenous rights in various Latin American countries, and security relations in the Middle East. With these thematic foci, we encourage graduate students to create and develop their own research by selecting a region of the world as their emphasis and adopting theoretically informed research and comparative methods that allow them to analyze the changing social and political conditions in the countries of this region.

American Politics The study of American Politics in the doctorate program in politics and international affairs provides a comprehensive overview as well as an in-depth analysis of American politics. Our faculty focus on various aspects of American politics, including theoretical foundations, federalism, institutions (Congress, the executive branch, the bureaucracy, the judiciary), political behavior (political parties, the media, interest groups, social movements, and elections), and public policy (foreign and domestic), and employ a range of methodological approaches such as historical development, legal doctrine, institutional rules, and quantitative analyses of the behavior of political actors and the mass public, to advance the student's research skills.  Our core class, Seminar in American Politics, for instance, surveys the key foundations, institutions, and behavior in American politics, introducing students to both qualitative and quantitative methodological approaches for analyzing and testing the changing trends and outcomes in American politics. Special topics courses provide opportunities to gain in-depth knowledge on new research on a range of themes, including political development, the social bases of politics, and the global impact of American politics. The faculty in American politics have made important contributions in the areas of race and ethnicity, the judiciary, the presidency, Florida government, civil liberties, health care, environmental justice, economic inequality, and animal rights. Our strengths lie in economic inequality, animal rights, the Presidency, Judicial Behavior, Race and Ethnicity, and State and Local Government. In these specific areas, we have published several cutting-edge books and articles in leading peer-reviewed journals, which examine the emergence and implementation of nonhuman animals' regime of rights, the changing directions of the U.S. Federal Reserve Bank and its impact on world politics, and alternative strategies for natural disasters in the United States. Our scholarship is thus distinctive for the ways in which it addresses American government and politics in a global context. This is how we seek to train our doctoral students on the rapidly changing, nuanced linkages between local, state, federal and global institutional politics.  

Political Theory Political Theory introduces students to the core normative issues in the study of political science. These normative issues provide the bedrock assumptions on which much of the study of political science depends. For example, while nearly everyone agrees that democracy is the best form of government, why do we place such faith in it? In addition, the long tradition of political thought offers multiple versions of democracy, each with its own strengths and limitations. How are we to identify the best version for our needs? Similarly, while we might extol non-violence in politics, is it always the best path for political movements? How are we to justify its alternatives? Clarifying our moral commitments, sharpening our conceptual tools, and outlining pathways for transforming theoretical knowledge into action requires philosophical, historical, and conceptual capabilities. The political theory faculty at the School of Interdisciplinary Global Studies trains students to develop these capabilities. To that end, political theory classes not only familiarize students with many of the canonical texts that were read by generations of prominent political thinkers (from Aristotle to Martin Luther King Jr), they also teach students to read these texts critically and with an eye towards contemporary political developments. As such, training in political theory is a critical supplement to graduate work at School of Interdisciplinary Global Studies. The faculty’s expertise in feminist theory, postcolonial theory, the role of emotions in politics, environmental political thought, and Indian political thought complements the terminal degrees offered in American Politics, Comparative Politics, and International Relations.

Financial Assistance 

Most of our successful applicants qualify for funding offered by the department or the Office of Graduate Studies. Funded doctoral students will receive a graduate assistantship that includes:

• a stipend for the academic year (9 months)
• a tuition waiver (not including school fees)
• the option of health insurance mostly paid by the department (the student only pays a small amount towards insurance).

All applicants for the doctoral degree are considered for a graduate assistantship - they do not need to complete a separate form.

The graduate assistantship is guaranteed for four years but is based on maintaining satisfactory annual academic progress. It requires each student to work 20 hours per week, in which case the student would be first assisting professors of the department with their teaching and class preparations and later, after having passed the doctoral comprehensive exams and completed teacher training seminars, teach a class at the University of South Florida. 

Please visit the graduate assistantships page for further information. The department also provides funding for conference travel or the presentation of research at conferences upon approval.

Information on eligibility for graduate assistantships can be found on the Graduate Assistantships Resource Center website. 

We also strive to fund our students in the fifth year, though this funding is not guaranteed. Depending on additional funds that become available, students may have the opportunity to extend their graduate assistantship to one, possibly two academic semesters. Students in the fifth year are also encouraged to seek external funding. For more information on this, please consult our Graduate Resources Page .

Outstanding candidates may also be nominated by the school’s director and/or graduate committee for prestigious and highly competitive university fellowships, including the Presidential Doctoral Fellowship , the Dorothy Auzenne Fellowship , and the University Graduate Fellowship. There is also the opportunity for minority students to be awarded a McKnight Fellowship, which provides annual tuition up to $5,000 for each of three academic years, plus an annual stipend of $12,000. The program also offers travel grants and other forms of financial support. For additional information on this fellowship opportunity, please visit the McKnight Fellowship's informational page.

• Politics and International Affairs Doctoral Handbook 2022 - 2023
• School of Interdisciplinary Global Studies Graduate Resources
• Independent Study / Directed Research Contract
• Office of Graduate Studies Forms
• Dissertation Proposal Approval Form
• Admission to Doctoral Candidacy Form
• Graduate Student Supervisory Committee Appointment Form
• Dissertation Checklist
• Electronic Thesis & Dissertation Certificate of Approval Form
• Comprehensive Exam Reading Lists
• Research Conference Travel Award Request
• Dissertation Defense Announcment

Spring 2024 Course Offerings

Recent Placements

For further information or questions about the PhD in Politics and International Affairs, please fill out this form . 

• Request Info

• James C. Kirkpatrick Library
• Campus Maps
• University Calendars

University of Central Missouri's Online Master’s in Computer Science Program Achieves Top Rankings for Affordability and Overall Excellence

By Alex Greenwood, May 2, 2024

WARRENSBURG, MO — The University of Central Missouri’s online Master of Science in Computer Science program is ranked #5 for affordability in TechGuide's 2024 list of Online Master’s in Computer Science degree programs. This ranking highlights the program’s commitment to providing high-quality education at an accessible price point, placing it among the top 25 institutions nationwide for affordability and value.

In addition to its affordability, the program also secured the #12 spot on TechGuide's list for the Best Online Master's in Computer Science degree programs for 2024, further underscoring its excellence in the competitive field of technology education.

The University of Central Missouri's HLC-accredited online master’s in computer science degree equips students with the skills necessary to lead in the tech industry, where professionals are increasingly essential across all sectors. As the largest and one of the most affordable programs in Missouri, UCM offers specialized tracks in cloud computing, general computer science and software development.

This flexibility ensures that graduates are not only proficient in using technology to solve diverse practical problems but are also prepared to lead teams and innovate in their chosen fields. While the program's courses are primarily available in person, students have the flexibility to customize their program options by pursuing their degree entirely online , on a full-time or part-time basis, accommodating various schedules and career goals.

Learn more about the program at the website: https://www.ucmo.edu/academics/programs/masters-degrees/chst/comp-sci-and-cybersecurity/computer-science/computer-science-masters/index.php .

TechGuide, a leading technology education resource platform, is renowned for its comprehensive coverage and expert insights in the technology sector, featuring contributions from esteemed professors and professionals through its "Ask an Expert" series and podcast, which includes more than 50 episodes with tech industry professionals. Learn more: https://techguide.org/computer-science/online-masters-in-computer-science/

social-section

An Invitation to Mathematical Logic

• David Marker 0

Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, Chicago, USA

You can also search for this author in PubMed   Google Scholar

• Offers a rigorous and inviting introduction to logic that inspires further study in logic
• Showcases connections to other areas of mathematics, including number theory, algebra, and combinatorics
• Versatile and appealing to graduate students in mathematics, computer science, and philosophy

Part of the book series: Graduate Texts in Mathematics (GTM, volume 301)

This is a preview of subscription content, log in via an institution to check access.

Access this book

• Durable hardcover edition
• Dispatched in 3 to 5 business days
• Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (16 chapters)

Front matter, truth and proof, languages, structures, and theories.

David Marker

Embeddings and Substructures

Formal proofs, gödel’s completeness theorem, elements of model theory, compactness and complete theories, ultraproducts, quantifier elimination, model theory of the real field, computability, models of computation, universal machines and undecidability, computably enumerable and arithmetic sets, turing reducibility, arithmetic and incompleteness, gödel’s incompleteness theorems, hilbert’s tenth problem, peano arithmetic and \( \epsilon _0\).

• Mathematical logic textbook
• Completeness theorem
• Incompleteness theorem
• Quantifier elimination
• Model theory introduction
• Computability introduction
• Hilbert's 10th problem
• graduate mathematical logic
• logic for philosophy
• logic for computer science
• quantifier elimination
• Godel's completeness
• ultraproducts
• Turing reducibility
• Godel's incompleteness
• Peano arithmetic

About this book

In addition to covering the essentials, the author’s intention in writing this text is to entice the reader to further study mathematical logic.  There is no current “standard text” for a first graduate course in mathematical logic and this book will fill that gap.   While there is more material than could be covered in a traditional one semester course, an instructor can cover the basics and still have the flexibility to choose several weeks’ worth of interesting advanced topics that have been introduced. The text can and will be used by people in various courses with different sorts of perspectives.  This versatility is one of the many appealing aspects of this book. A list of suggested portions to be covered in a single course is provided as well as a useful chart which maps chapter dependencies. Additionally, a motivated student will have ample material for further reading.

New definitions, formalism, and syntax have been streamlined to engage thereader quickly into the heart of logic and to more sophisticated topics. Part I and Part IV center on foundational questions, while Part III establishes the fundamentals of computability. Part II develops model theory, highlighting the model theory of the fields of real and complex numbers. The interplay between logic and other areas of mathematics, notably algebra, number theory, and combinatorics, are illustrated in Chapters 5, 6, 8, 14, and 16.  For most of the text, the only prerequisite is mathematical maturity. The material should be accessible to first year graduate students or advanced undergraduates in mathematics, graduate students in philosophy with a solid math background, or students in computer science who want a mathematical introduction to logic. Prior exposure to logic is helpful but not assumed.

Authors and Affiliations

About the author.

David Marker is Professor Emeritus of Mathematics at the University of Illinois at Chicago where he was Liberal Arts & Sciences Distinguished Professor and a Fellow of the American Mathematical Society. His research interests lie in model theory and its applications. His textbook, Model Theory: An Introduction , which appeared as GTM 217 in 2002, was awarded the Association of Symbolic Logic Shoenfield Prize for expository writing.

Bibliographic Information

Book Title : An Invitation to Mathematical Logic

Authors : David Marker

Series Title : Graduate Texts in Mathematics

DOI : https://doi.org/10.1007/978-3-031-55368-4

Publisher : Springer Cham

eBook Packages : Mathematics and Statistics , Mathematics and Statistics (R0)

Copyright Information : The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2024

Hardcover ISBN : 978-3-031-55367-7 Published: 07 May 2024

Softcover ISBN : 978-3-031-55370-7 Due: 07 June 2024

eBook ISBN : 978-3-031-55368-4 Due: 07 June 2024

Series ISSN : 0072-5285

Series E-ISSN : 2197-5612

Edition Number : 1

Number of Pages : XVIII, 357

Number of Illustrations : 7 b/w illustrations

Topics : Mathematical Logic and Foundations

• Publish with us

Policies and ethics

• Find a journal
• Track your research

College of Liberal Arts & Sciences

Department of Philosophy

• Why Philosophy?
• Career Paths in Philosophy
• What Can You Do with a Philosophy Degree?
• Undergraduate Admission and Application
• Graduate Admission and Application
• Student Financial Aid
• Alumni Spotlights
• Visit Illinois
• Undergraduate Studies
• Graduate Studies
• Course Descriptions
• Philosophy Colloquium Series
• Areas of Specialization
• Ancient Greek Philosophy
• Artificial Intelligence
• Biomedical Ethics
• Decision Theory
• Epistemology
• Experimental Philosophy
• Feminist Philosophy
• Metaphysics
• Modern Philosophy
• Moral Psychology
• Philosophy of Law
• Philosophy of Language
• Philosophy of Logic and Math
• Philosophy of Mind and Cognitive Science
• Philosophy of Psychology
• Philosophy of Religion
• Philosophy of Science
• Philosophy of Sex, Love, and Gender
• Social and Political Philosophy
• Faculty Publications
• Administration & Staff
• Graduate Students
• Illinois Philosophy Guiding Principles
• Department Bylaws
• Wellness Resources
• Campus Resources
• Graduate Student Resources
• Affiliated Philosophical Organizations
• Awards and Scholarships
• Minorities and Philosophy (MAP) Chapter
• Stay Connected With Us
• Colloquium Series
• Donate to Philosophy

Philosophy + CS undergraduate Max Fan awarded National Science Foundation Graduate Research Fellowship

Max Fan, a junior Philosophy + CS major, has recently been awarded a National Science Foundation Graduate Research Fellowship   which will provide three years of financial support for his graduate studies. Fan will graduate this May and begin his PhD at Cornell University in the fall.  

While at the University of Illinois, and during a summer internship at NASA in 2023, Fan proposed and developed a new temporal logic semantics, a topic he first encountered in a class taught by philosophy professor Kohei Kishida.  

Temporal logic is a system of rules for representing and reasoning about propositions that change over time. In computer science, and at NASA, it’s used to specify when safety conditions should be triggered and to determine when a system is behaving nominally.  

“They don’t like bugs, and they don’t like things going wrong,” Fan said. “And so, the idea is you have all these requirements for how your rocket or how your satellite ought to behave. So, if your satellite does this, it should then do this, and these logics have a temporal nature.”  

For example, a temporal property might say “after the parachute deploys then the machine should decelerate.” Once the temporal property is specified, it is important to monitor the system to verify if it is behaving as expected. When a property is violated, the error should be handled as quickly as possible. 

Fan soon recognized that the standard temporal logic semantics that most people in computer science work with were not sufficient for NASA’s purposes. His coursework in philosophy helped him realize he could develop his own semantics that better captured the problem he was trying to solve.  

“My philosophical training allowed me to think outside the box and develop a different way that didn’t rely on the standard approaches,” he said. “I think there’s a reason why no one else thought of this before because people generally take the standard temporal logic semantics and do other things with it. But they don’t think about changing the actual ground rules.” 

He proposed a non-standard temporal logic semantics that will work better to solve NASA’s and other computer science problems. He has a paper in progress that he is hoping to submit to a conference soon.  

Fan also regularly seeks out perspectives on logic from researchers working in fields outside his major. He organizes a weekly lunch for those working on logic in computer science that also attracts professors and students in philosophy, electrical and computer engineering, and math. 

“The idea is that people who are interested in logic or logic adjacent come and talk about research and what people are working on,” he said. “It’s quite nice to see everyone and to hear about a different perspective. The math department has a certain kind of flavor of the research, which is a little different than the philosophy department, which is different than the flavor in the CS department.” 

Fan’s research interests include the intersection of computer science and philosophy, epistemology, and logic and truth, which is why he decided to major in philosophy + CS . In addition to professor Kishida, he also cites philosophy professor Jonathan Livengood, and computer science professor Talia Ringer as mentors during his time at the university.  

The NSF fellowship is not the first accolade he has received for his work. In his sophomore year, he received a Barry M. Goldwater scholarship for his potential to contribute to the advancement of research in the natural sciences, mathematics, or engineering. A fellow philosophy junior, Sylvia E, was also recently honored with a Goldwater Scholarship.   

His favorite courses have been the graduate seminars he has participated in, including the philosophy of logic graduate seminar, which he took twice, and the conceptual engineering seminar taught by philosophy professor Kevin Scharp. 

“I think all the courses [in philosophy] are actually very well taught. Like some departments are hit and miss. But every course here has been a hit. …The quality of instruction is quite high,” he said.