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University of Colorado Boulder Admissions

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University of Colorado Boulder Acceptance Rates & Admissions Statistics

What does the admissions department at university of colorado boulder look for in an applicant.

Utilize the admission data from the most recent freshman classes at University of Colorado Boulder to evaluate how you measure up.

On this page you’ll find:

What Admissions Stats Mean for You

Selectivity of University of Colorado Boulder

Acceptance & Enrollment Stats at University of Colorado Boulder

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What Admissions Statistics Mean for You?

Reviewing the admissions stats at University of Colorado Boulder can help you determine your likelihood of acceptance. Take a look at the SAT and ACT scores of previous applicants to help you understand your chances of being accepted. If you find your scores are lower than the average freshman, try retaking the exam to better your score or reviewing colleges looking for scores matching your own.

Looking for University of Colorado Boulder application deadlines and requirements?

Selectivity (Fall 2021): Are You the Right Type of Student For This College?

Acceptance and enrollment stats (fall 2021), who’s applying: applicants by gender, average test scores.

About 32% of students accepted to CU - Boulder submitted their SAT scores. When looking at the 25th through the 75th percentile, SAT Evidence-Based Reading and Writing scores ranged between 590 and 690. Math scores were between 580 and 700.

CU - Boulder received ACT scores from 16% of accepted students. When looking at the 25th through the 75th percentile, ACT Composite scores ranged between 25 and 31.

Additional Question to Ask

A college’s selectivity gives us an idea of how rigorous the studies are, and how competitive the students are. However, not all students thrive in a competitive atmosphere, even if their grades are good. Does this college have the best learning environment for you?

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University of Colorado Boulder Admissions

University of Colorado Boulder admissions has an acceptance rate of 79% and an early acceptance rate of 93.7%. Half the applicants admitted to University of Colorado Boulder who submitted test scores have an SAT score between 1160 and 1390 or an ACT score of 26 and 31. However, one quarter of admitted applicants achieved scores above these ranges and one quarter scored below these ranges. The application deadline at University of Colorado Boulder is Jan. 15.

Admissions officials at University of Colorado Boulder consider a student's GPA a very important academic factor. An applicant's high school class rank, when available, is considered and letters of recommendation are considered important for admissions officials at University of Colorado Boulder. To see additional academic factors along with other school data, learn more about College Compass .

University of Colorado Boulder Admissions Stats

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University of Colorado Boulder (CU Boulder)

University of Colorado Boulder can be found in Boulder, CO, a public college which focuses on only a select few programs offered. CU Boulder has around 39,000 students enrolled yearly.

Many of the students that got into CU Boulder got an SAT score between 1140 - 1360, or got accepted with an ACT composite score within the range of 25 - 31. Based on sampled GPA data collected and applied, it is estimated that the CU Boulder average GPA range for accepted students is around 3.42 - 3.71. CU Boulder has an acceptance rate of about 78% with 22% of applicants deciding to attend. Using acceptance rate data from previous years, we can project that the CU Boulder acceptance rate in 2021 is going to be around 74%. You can get more information from the admissions office website at colorado.edu .

Overall CU Boulder Acceptance Rate - Fall 2020

The overall acceptance rate for University of Colorado Boulder was reported as 78.4% in Fall 2020 with over 40,700 college applications submitted to University of Colorado Boulder. Both in state and out of state applicants are included in these figures. We do not have data on transfer acceptance rates currently.

Accepted Applicants Profile

CU Boulder ACT Scores: 25 - 31
CU Boulder Average GPA: 3.42 - 3.71

How Hard Is It to Get into University of Colorado Boulder?

Applicant selectivity: high.

The selectivity of applicants for undergraduate admissions to CU Boulder is considered high, with many applicants scoring in the top percentiles on the SAT or ACT exam, as well as having an excellent high school GPA.

Historical Trend and Acceptance Rate 2024 Projection

Acceptance rate by year.

2016-2017: 76.6%
2017-2018: 79.8%
2018-2019: 81.5%
2019-2020: 78.4%
Projected CU Boulder Acceptance Rate 2024-2025: 73.8%

How Does CU Boulder Compare?

The acceptance rate for University of Colorado Boulder is thirty-eight percent higher than the national average of all colleges which is around 56.7%.

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Gre prep online guides and tips, graduate school acceptance rates: can you get in.

Even the most qualified and confident applicants worry about getting into grad school. But don’t panic! Graduate school acceptance rates, which give the percentage of applicants that were admitted to a particular school or program in an academic year, can help you determine how likely you are to get into a given program. But where can you find grad school admissions statistics?

In this article, we’ll first investigate the trends and factors associated with graduate school acceptance rates. Then, we’ll take a look at some of the current acceptance rates and give you expert tips on how to find acceptance rates for your programs. Finally, we’ll show you how to determine your odds of getting into grad school.

Graduate School Acceptance Rates: Factors and Trends

Grad school acceptance rates are the same as any other acceptance rate: the lower the acceptance rate, the more selective the school or program is. Similarly, the higher the acceptance rate, the less selective the school or program is. As with undergrad acceptance rates, grad school acceptance rates vary widely, from extraordinarily selective (less than 5 percent) to incredibly lenient (nearly 100 percent).

Unlike undergrad rates, though, grad school acceptance rates are usually calculated for specific programs or departments and not for entire universities. This is because with grad school, you are essentially applying to an individual program rather than an overall institution (as you did for undergrad).

Now that we’ve covered all of the basics, let’s look at a few key trends. Our research indicates there are three major factors that help determine grad school acceptance rates:

School or program prestige
Degree type
Amount of funding

Let’s look at how each of these factors influences grad school acceptance rates.

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#1: School or Program Prestige

How prestigious a particular grad school or program is can affect its overall competitiveness and selectivity. In general, the more prestigious a program is, the more competitive it’ll be and thus the lower acceptance rate it’ll have.

An easy way to determine school or program prestige is to consult official rankings, such as those listed on U.S. News . (Grad schools are typically ranked by field or program and not by overall institution.)

For example, a 2017 U.S. News list of the best political science grad programs ranked Duke’s political science program at #7 and Northwestern’s at #23. Because both of the programs have fairly high rankings, it’s safe to assume they’re probably quite selective.

And this is true: in 2016, Duke reported a mere 10 percent acceptance rate to its political science doctoral program, while Northwestern reported a 12 percent acceptance rate.

#2: Degree Type

Another major factor is degree type. Generally, doctoral programs tend to be more selective than master’s programs (though this isn’t always the case as I’ll explain in a moment). This trend is likely due to the fact that doctoral programs often look for higher-quality applicants with proven academic track records and more relevant experience in their fields.

For example, in 2016 University of Michigan’s math doctoral program had a 17.2 percent acceptance rate, whereas its master’s program had a much higher 31.8 percent rate. In this case, the doctoral program is clearly tougher to get into than the master’s program.

Still, master’s programs can have lower acceptance rates than doctoral programs. If we were to take the University of Michigan’s grad programs in computer science and engineering, we’d find that the doctoral program has a 15 percent acceptance rate and the master’s an even lower 8 percent acceptance rate .

Additionally, M.F.A. programs are particularly cutthroat. In 2015, the creative writing M.F.A. program at UT Austin’s James A. Michener Center for Writers only admitted 12 out of 678 applicants — that’s a mere 1.8 percent acceptance rate !

#3: Amount of Funding

Funding, too, plays a big role in how selective a grad program is.

Well-funded programs typically receive more applications than those offering little to no aid, thereby raising their selectivity. Competition is especially fierce for fully funded programs — possibly because fewer people are willing to go into debt for grad school.

Compared to fully funded doctoral programs, fully funded master’s programs are somewhat rare and thus pretty competitive. UT Austin’s Creative Writing M.F.A. program, for instance, is not only a prestigious program but also one of the most well-funded Creative Writing M.F.A. programs in the country: it offers full tuition remission and a $27,500 stipend per academic year . It’s no wonder, then, that its acceptance rate is below 2 percent!

What Are the Current Graduate School Acceptance Rates?

For this section, we’ve scoured the internet to bring you a robust assortment of acceptance rates for popular U.S. grad schools.

Before we dive in, note that not all institutions calculate grad school acceptance rates using the same methodologies. Some offer only a single acceptance rate for all of their grad schools put together, while others offer individual rates by school, field, or program.

Now, let’s see how selective these schools really are!

*Statistics for NYU are based on the number of enrolled students and not the number of admitted students. Therefore, expect actual acceptance rates to be slightly higher.

How to Find Graduate School Acceptance Rates: 4 Methods

Unfortunately, grad school admissions statistics tend to be more difficult to find than undergrad acceptance rates. But there are ways to search for them — you just have to do a lot of digging and possibly a little reaching out.

Below are our top four methods for finding grad school acceptance rates for the programs you’re applying to.

#1: Consult School Websites

By far the most reliable resources for grad school admissions statistics are school websites.

Start your search by consulting program and departmental pages, particularly admissions and FAQ pages. Look out for any statistics-related keywords or phrases, such as “admission(s) rates,” “acceptance rates,” “enrollment,” “facts and figures,” etc. Use ctrl+F to move swiftly through large chunks of text.

Not all schools publish grad admissions information online, and those that do don’t always report it in the same way as others. For example, Princeton offers a handy PDF containing acceptance rates for all academic fields of study. On the other hand, Notre Dame gives separate admissions charts for each of its grad programs (which you can access by selecting a program and then clicking “Admissions Statistics”).

Additionally, many schools release admissions statistics without explicitly publishing acceptance rates. In this case, it’s your job to take the statistics provided and use them to calculate an acceptance rate. To find the acceptance rate of a school or program, you’ll need the following information:

The total number of applicants in a year
The total number of applicants granted admission that year

The acceptance rate equals the total number of applicants offered admission divided by the total number of applicants and then multiplied by 100, or:

$$\acceptance \rate = {\number \of \applicants \offered \admission}/{\total \number \of \applicants}100$$

Be sure to avoid conflating the number of students who were offered admission with the number of students who accepted their offers of admission. These two concepts sound alike but are actually different. What you’re looking for is the first statistic — that is, the number of admitted students (regardless of whether they decided to enroll).

If you’re having trouble finding admissions statistics by browsing school websites, search on Google for “[Your School] graduate acceptance rate” and see if any relevant school pages appear. While searching for acceptance rates to use in the table above, I consistently swapped “acceptance rate” with similar phrases, such as “admission(s) rate,” “facts and figures,” “student statistics,” “admittance rates,” and “admission(s) statistics.”

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Don’t be afraid to get creative! You can also use phrases like “Ph.D. admissions statistics” or “master’s admissions statistics” to narrow your search even further. Try to think outside the box as you do your research. What are other ways people talk about acceptance rates?

#2: Check U.S. News

If your school or program doesn’t offer any admissions statistics on its website, go to U.S. News . This website offers official rankings of grad programs as well as lists of the most (and least) selective programs in various fields.

For example, I found a 2016 list of the most competitive online M.B.A. programs and a 2015 list of the most competitive online graduate engineering programs .

If U.S. News doesn’t offer any relevant lists for you to use, try skimming the current grad school rankings to gauge how competitive your program is compared with others in the same field.

#3: Search Other Websites

One less reliable method for looking up grad school admissions statistics is to look for (unofficial) websites discussing acceptance rates for your school or program.

The Grad Cafe’s admissions results section is a solid place to start. Here, applicants post whether they’ve been accepted, rejected, or waitlisted for grad programs.

Search for your program to get a rough feel for how many acceptances and rejections go out each year. You might notice that certain types of applicants are more active than others. Creative Writing M.F.A. applicants, for example, are prolific posters in winter and spring (during admissions season).

Occasionally, Google itself will provide you with grad school acceptance rates, but this only appears to work consistently for well-known law schools, medical schools, and business schools.

Additionally, while using Google, don’t assume that any acceptance rates that pop up are directly connected to your search terms. For example, when I searched “stanford graduate acceptance rate,” Google gave me this result:

This 4.8 percent acceptance rate is not the acceptance rate for Stanford’s grad programs (what I searched for) but rather the acceptance rate for undergrads. So always cross-check any statistics Google gives you.

You can also consult grad school data websites such as Peterson’s and StartClass . Take their grad school acceptance rates with a grain of salt, though — their data isn’t always verifiable online. If possible, try to compare any data you find on these types of websites with the school websites themselves or U.S. News .

#4: Contact Schools

If the internet isn’t giving you the help you need, call or email your schools. Be polite but upfront: ask whether the school calculates acceptance rates for grad programs and where you can find this information online (if available).

If a school refuses to divulge admissions statistics or simply doesn’t report acceptance rates, see if they can give you estimates for how many applications they receive each year, or for how many acceptances they usually extend to applicants in your program.

Graduate School Acceptance: What Are Your Odds?

By this point, you might be wondering how likely it is you’ll actually get into the grad program you wish to attend. After all, acceptance rates are pretty broad — they tell you what everyone’s odds are but not your odds specifically.

Below are three easy steps for determining your odds of getting into grad school, including advice on when it’s better to go for it or choose another program.

Step 1: Check Program Requirements

First, go to your program’s website and pinpoint the admissions requirements page. Now, ask yourself: do you meet all of the program’s basic requirements? If not, you’ll likely wind up with a rejection (and might not even be able to apply).

However, if you’re still interested in applying, contact the program and ask if they’ll make an exception for you. Your chance of getting accepted is still low, but you’ll at least have your application considered.

If your program strongly recommends qualities you lack, don’t interpret this as an automatic rejection. Sometimes, applicants can make up for deficiencies in other ways. For example, if your undergrad GPA is 3.1 and your program recommends applicants have a minimum 3.2, don’t write off the program — you might still have a shot at getting in as long as the rest of your application is solid.

On the other hand, even if you meet all of a program’s requirements, you’re not necessarily a shoo-in. Remember, all other applicants have met these requirements, too, so you’ll need to find a unique way to make your application stand out.

Step 2: Find Average GRE Scores and GPAs

Your next step is to look up your program’s average GRE scores and GPA to see how your own scores and GPA compare with those of previously admitted applicants.

You can usually find GRE score information on admissions requirements or FAQ pages. You can also search on Google for “[Your School] [Your Program] average GRE scores.” For step-by-step instructions on how to find average GRE scores, check out my article on average GRE scores by school .

For GPAs, you can use the same basic methodology. Check admissions requirements and FAQ pages and use ctrl+F to search for “GPA.” If GPA information is available, you’ll most likely come across minimum GPAs or average GPAs (or both). For more tips on how to find GPA information for your grad schools, read our guide .

Now, compare your own GRE scores and GPA with the averages you’ve found. Below are all possible scenarios and what they mean for you and your odds of getting into the program:

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Your GRE scores and GPA are both higher than your program’s averages: Congratulations! You have an excellent chance of getting accepted, especially if the rest of your application is equally impressive. Keep up the great work!
Your GRE scores and GPA are both about the same as your program’s averages: You’re doing pretty well! You are just the type of applicant your program is looking for. The only drawback is that you probably won’t stand out as much from other applicants who have similar GRE scores and GPAs. So take time to make your application sparkle (I’m looking at you, statement of purpose).
Your GRE scores and GPA are both lower than your program’s averages (or just one of the two is lower): It ain’t over ’til it’s over! You can still make up for your deficiencies in other ways. While you can’t change your GPA, you can retake the GRE . If your GPA is low, a great strategy for combating this is to discuss it in your statement of purpose, taking care to highlight any external factors that contributed to the low GPA as well as any attributes of yours that prove you’re indeed ready for grad school.

Step 3: Decide Whether to Apply

Now, we get to the final question: do you apply to the program or not? This is a vague question that’s difficult to answer as is. The real questions you should be asking yourself are as follows:

Do I meet all of the program’s basic requirements?
Do I meet most or all of the program’s expectations of applicants (in terms of GRE scores, GPA, etc.)?
Is the program’s acceptance rate extremely low?
Do I really like this program?

Although acceptance rates and GRE/GPA comparisons are helpful, don’t base your decision to apply solely on how difficult the program is to get into. We can’t know for sure what kind of applicant a grad program is looking for or who they’re willing to make an exception for.

Take a moment to think deeply about how interested you are in this particular program. Be realistic about your chances of getting in — but don’t cross the line into pessimism. If you don’t meet most or all of a program’s expectations and you’re not super invested in it, consider applying elsewhere.

But if you meet some, most, or all of a program’s expectations and you’re extremely interested in enrolling, give the application a go. Remember, it’s totally normal (and even encouraged) to have a few reach schools. Plus, you’ll never get in if you don’t apply!

Key Takeaways: Graduate School Acceptance Rates

Grad school acceptance rates quantify for us the selectivity of grad schools and programs. More specifically, acceptance rates tell us what percentage of applicants were offered admission to a particular grad school or program.

With grad school, acceptance rates are often reported for individual schools or programs, not entire universities. Acceptance rates can vary widely depending on program prestige, the type of degree you’re seeking, and how much (or how little) funding a program offers.

Unlike undergrad acceptance rates, grad school acceptance rates are somewhat difficult to locate online. You can look for them using any of the following four methods:

Peruse school websites
Check grad school facts and lists on U.S. News
Browse other websites and forums such as The Grad Cafe
Call or email your schools

When trying to determine your odds of getting into a program, look at your program’s requirements as well as the average GPA and GRE scores of previously admitted applicants to your program. If your GRE scores and GPA are comparable to those of your program, you have a decent shot at getting accepted. If one or both are lower than your program’s averages, however, you can always try to raise your GRE score with a retake or address your GPA in your statement of purpose.

At the end of the day, what ultimately matters isn’t that you get accepted to a highly competitive grad program but that you make the right decision for you and you alone!

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Hannah graduated summa cum laude from the University of Southern California with a bachelor’s degree in English and East Asian languages and cultures. After graduation, she taught English in Japan for two years via the JET Program. She is passionate about education, writing, and travel. View all posts by Hannah Muniz

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PhD in Applied Mathematics

Our PhD in Applied Mathematics program provides comprehensive training in applied mathematics and/or statistics and opportunities for cutting-edge research in close collaboration with internationally recognized scholars in the fields of

Computational Mathematics
Discrete Mathematics
Optimization and Operations Research
Probability

Some highlights of our exciting research projects include evolutionary dynamics, climate modeling, wildfire simulations, machine learning, genetic inheritance and association, optimization in data analysis, and more. Current research funding includes grants from NSF, NIH, DoD, and NASA.

The degree is designed to give students a contemporary, comprehensive education in subjects such as high-performance computing, numerical analysis, optimization, statistical methods, and operations research. In all of its activities, the department embodies the outlook that mathematics, statistics, computing, and data science are powerful tools that can be used to solve problems of immediate and practical importance. Our program emphasizes the training of skills valued by many employers. These skills include problem solving, critical thinking, analysis, facility with data, the ability to process quantitative information, and most important of all, the ability to learn and master new skills and concepts quickly. These strengths make our students highly marketable for careers in industry as well as in academia. Scholarships and assistantships for graduate students are available and awarded competitively.

Graduate Program Director

Florian Pfender [email protected]

Director of Statistical Programs

Daniel Klie [email protected]

General Inquiries

Miriam Venzor Program Assistant [email protected] Phone: 303-315-1702

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Your chance of acceptance, your chancing factors, extracurriculars, what's the acceptance rate for boulder.

Hey everyone, I'm looking into applying to the University of Colorado Boulder. Before I commit to writing my essay, I wanted to know the acceptance rate. Does anyone know it for the most recent admission cycle? Thanks in advance!

The acceptance rate for the University of Colorado Boulder in the most recent admission cycle was around 79%. Keep in mind that acceptance rates can vary from year to year, but this should give you a rough idea of the level of selectivity at CU Boulder. Good luck with your application!

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Mathematics (MATH)

MATH 1005 (3) Introduction to College Mathematics

Introductory level mathematics course which presents a college level introduction to algebraic functions and their applications. Only offered through the Student Academic Service Center.

Equivalent - Duplicate Degree Credit Not Granted: MATH 1011 Additional Information: MAPS Course: Mathematics

MATH 1011 (3) College Algebra

Covers simplifying algebraic expressions, factoring, linear and quadratic equations, inequalities, exponentials, logarithms, functions, graphs and systems of equations. Department enforced prerequisite: one year high school algebra.

Equivalent - Duplicate Degree Credit Not Granted: MATH 1005 Additional Information: Arts Sci Core Curr: Quant Reasn Mathmat Skills Arts Sci Gen Ed: Quantitative Reasoning Math MAPS Course: Mathematics

MATH 1012 (3) Quantitative Reasoning and Mathematical Skills

Promotes mathematical literacy among liberal arts students. Teaches basic mathematics, logic, and problem-solving skills in the context of higher level mathematics, science, technology, and/or society. This is not a traditional math class, but is designed to stimulate interest in and appreciation of mathematics and quantitative reasoning as valuable tools for comprehending the world in which we live.

Equivalent - Duplicate Degree Credit Not Granted: MATH 1112 Additional Information: GT Pathways: GT-MA1 - Mathematics Arts Sci Core Curr: Quant Reasn Mathmat Skills Arts Sci Gen Ed: Quantitative Reasoning Math MAPS Course: Mathematics

MATH 1021 (3) College Trigonometry

Covers trigonometric functions, identities, solutions of triangles, addition and multiple angle formulas, inverse and trigonometric functions and laws of sines and cosines. Department enforced prerequisite: MATH 1011 (minimum grade C-) or 1 1/2 years of high school algebra and 1 year of high school geometry.

Equivalent - Duplicate Degree Credit Not Granted: APPM 1235 or MATH 1150

MATH 1071 (3) Finite Mathematics for Social Science and Business

Discusses systems of linear equations and introduces matrices, linear programming, and probability.

Requisites: Requires prerequisite course of MATH 1011 (minimum grade C-) or a score of 46% or greater on an ALEKS math exam taken in 2016 or earlier. Additional Information: Arts Sci Core Curr: Quant Reasn Mathmat Skills Arts Sci Gen Ed: Quantitative Reasoning Math

MATH 1081 (3) Calculus for Social Science and Business

Covers differential and integral calculus of algebraic, logarithmic and exponential functions. For more information about the math placement referred to in the "Enrollment Requirements", contact your academic advisor.

Equivalent - Duplicate Degree Credit Not Granted: APPM 1345 or APPM 1350 or ECON 1088 or MATH 1300 or MATH 1310 or MATH 1330 Requisites: Requires prerequisite course of ECON 1078 or MATH 1011 or MATH 1071 or MATH 1150 or MATH 1160 (minimum grade C-) or an ALEKS math exam taken in 2016 or earlier, or placement into pre-calculus based on your admission data and/or CU Boulder coursework. Additional Information: Arts Sci Core Curr: Quant Reasn Mathmat Skills Arts Sci Gen Ed: Quantitative Reasoning Math

MATH 1110 (3) Mathematics for Elementary Educators 1

Includes a study of problem solving techniques in mathematics and the structure of number systems. Department enforced prereq., one year of high school algebra and one year of geometry. Department enforced restriction: restricted to prospective elementary teachers.

Additional Information: Arts Sci Core Curr: Quant Reasn Mathmat Skills Arts Sci Gen Ed: Quantitative Reasoning Math

MATH 1112 (4) Mathematical Analysis in Business

Gives students experience with mathematical problem solving in real business contexts. Students will work with data and spreadsheets to build and analyze mathematical models. Themes of the course include applying logical operators to model business rules, interpreting data and using tables and graphs, finding break-even and optimal points, and addressing uncertainty and forecasting

Equivalent - Duplicate Degree Credit Not Granted: MATH 1012 Additional Information: Arts Sci Core Curr: Quant Reasn Mathmat Skills Arts Sci Gen Ed: Quantitative Reasoning Math MAPS Course: Mathematics

MATH 1120 (3) Mathematics for Elementary Educators 2

Topics include geometry, measurement, probability, and statistics. Department enforced restriction: restricted to prospective elementary teachers.

Requisites: Requires prerequisite course of MATH 1110 (minimum grade C-). Additional Information: Arts Sci Core Curr: Quant Reasn Mathmat Skills Arts Sci Gen Ed: Quantitative Reasoning Math

MATH 1130 (3) Mathematics from the Visual Arts

Introduces mathematical concepts through the study of visual arts.

MATH 1150 (4) Precalculus Mathematics

Develops techniques and concepts prerequisite to calculus through the study of trigonometric, exponential, logarithmic, polynomial and other functions. For more information about the math placement referred to in the "Enrollment Requirements", please contact your academic advisor.

Equivalent - Duplicate Degree Credit Not Granted: APPM 1235 or MATH 1021 Requisites: Requires prerequisite course of MATH 1011 (minimum grade C-) or an ALEKS math exam taken in 2016 or earlier, or placement into pre-calculus based on your admissions data and/or CU Boulder coursework. Requires enrollment in corequisite course MATH 1151 . Additional Information: GT Pathways: GT-MA1 - Mathematics Arts Sci Core Curr: Quant Reasn Mathmat Skills Arts Sci Gen Ed: Quantitative Reasoning Math MAPS Course: Mathematics

MATH 1151 (1) Precalculus Supplemental Lab

Provides students concurrently enrolled in MATH 1150 with supplemental instruction.

Requisites: Requires enrollment in corequisite course of MATH 1150 . Grading Basis: Letter Grade

MATH 1160 (3) Transition to Calculus (IBL): The Theory, Applications and Analysis of Functions

Examines the functions of calculus and how they can be used to model concrete problems and/or change. This is an intensive study of these functions through Inquiry-Based Learning. Each class will be designed so students will be actively engaged in learning the material in small groups. For more information about the math placement referred to in the "Enrollment Requirements", please contact your academic advisor.

Requisites: Requires an ALEKS math exam taken in 2016 or earlier, or placement into pre-calculus based on your admissions data and/or CU Boulder coursework.

MATH 1212 (3) Data and Models

Engages students in statistical and algebraic problem solving through modeling data and real world questions taken from the social and life sciences. The course will emphasize these skills and the mathematical background needed for a university level statistics course.

Equivalent - Duplicate Degree Credit Not Granted: MATH 1011 Grading Basis: Letter Grade Additional Information: Arts Sci Core Curr: Quant Reasn Mathmat Skills Arts Sci Gen Ed: Quantitative Reasoning Math MAPS Course: Mathematics

MATH 1300 (5) Calculus 1

Topics include limits, derivatives of algebraic and transcendental functions, applications of the derivative, integration and applications of the definite integral. Students who have already earned college credit for calculus 1 are eligible to enroll in this course if they want to solidify their knowledge base in calculus 1. For more information about the math placement referred to in the "Enrollment Requirements", contact your academic advisor.

Equivalent - Duplicate Degree Credit Not Granted: APPM 1345 or APPM 1350 or ECON 1088 MATH 1081 or MATH 1310 or MATH 1330 Requisites: Requires prerequisite course of MATH 1011 and MATH 1021 or MATH 1150 or MATH 1160 or APPM 1235 (minimum grade C-) or an ALEKS math exam taken in 2016 or earlier, or placement into calculus based on your admissions data and/or CU Boulder coursework. Additional Information: GT Pathways: GT-MA1 - Mathematics Arts Sci Core Curr: Quant Reasn Mathmat Skills Arts Sci Gen Ed: Quantitative Reasoning Math

MATH 1301 (1) Calculus 1 Supplemental Lab

Provides students concurrently enrolled in MATH 1300 with supplemental instruction.

Requisites: Requires corequisite course of MATH 1300 . Grading Basis: Letter Grade

MATH 1310 (5) Calculus for Life Sciences

Calculus concepts are developed through the analysis and modeling of complex systems, ranging from gene networks and cells to populations and ecosystems. Fundamental concepts of probability and statistics are also developed through the lens of calculus. MATH 1300 is similar, but a greater emphasis is placed on relevance and applications in biology and other life sciences. Students who have already earned college credit for calculus 1 are eligible to enroll in this course if they want to solidify their knowledge base in calculus 1. For more information about the math placement referred to in the "Enrollment Requirements", contact your academic advisor.

Equivalent - Duplicate Degree Credit Not Granted: APPM 1345 or APPM 1350 or ECON 1088 or MATH 1081 or MATH 1300 or MATH 1330 Requisites: Requires prerequisite course of APPM 1235 or MATH 1021 or MATH 1150 or MATH 1160 or MATH 1300 (minimum grade C-) or an ALEKS math exam taken in 2016 or earlier, or placement into calculus based on your admissions data and/r CU Boulder coursework. Additional Information: GT Pathways: GT-MA1 - Mathematics Arts Sci Core Curr: Quant Reasn Mathmat Skills Arts Sci Gen Ed: Quantitative Reasoning Math

MATH 1330 (4) Calculus for Economics and the Social Sciences

A calculus course intended to meet the needs of social science and economics majors, including applications. Covers differential and integral calculus of algebraic, logarithmic and exponential functions and modeling. For more information about the math placement referred to in the "Enrollment Requirements", contact your academic advisor.

Equivalent - Duplicate Degree Credit Not Granted: APPM 1345 or APPM 1350 or ECON 1088 or MATH 1081 or MATH 1300 or MATH 1310 Requisites: Requires a prerequisite course of ECON 1078 or MATH 1011 or MATH 1071 or MATH 1150 or MATH 1160 (minimum grade C-) or an ALEKS math exam taken in 2016 or earlier, or placement into calculus based on your admissions data and/r CU Boulder coursework. Additional Information: Arts Sci Core Curr: Quant Reasn Mathmat Skills Arts Sci Gen Ed: Quantitative Reasoning Math

MATH 2001 (3) Introduction to Discrete Mathematics

Introduces the ideas of rigor and proof through an examination of basic set theory, existential and universal quantifiers, elementary counting, discrete probability, and additional topics.

Equivalent - Duplicate Degree Credit Not Granted: MATH 2002 Requisites: Requires prerequisite course of MATH 1300 or MATH 1310 or APPM 1345 or APPM 1350 (all minimum grade C-).

MATH 2002 (3) Number Systems: An Introduction to Higher Mathematics

Introduces the concepts of mathematical proofs using the construction of the real numbers from set theory. Topics include basic logic and set theory, equivalence relations and functions, Peano's axioms, construction of the integers, the rational numbers and axiomatic treatment of the real numbers.

Equivalent - Duplicate Degree Credit Not Granted: MATH 2001 Requisites: Requires prerequisite of MATH 1300 or MATH 1310 or APPM 1345 or APPM 1350 (all minimum grade C-).

MATH 2130 (3) Introduction to Linear Algebra for Non-Mathematics Majors

Examines basic properties of systems of linear equations, vector spaces, inner products, linear independence, dimension, linear transformations, matrices, determinants, eigenvalues, eigenvectors and diagonalization. Intended for students who do not plan to major in Mathematics. Formerly MATH 3130 .

Equivalent - Duplicate Degree Credit Not Granted: MATH 2135 or APPM 3310 Requisites: Requires prerequisite course of MATH 2300 or APPM 1360 (minimum grade C-).

MATH 2135 (3) Introduction to Linear Algebra for Mathematics Majors

Equivalent - Duplicate Degree Credit Not Granted: MATH 2130 or APPM 3310 Requisites: Requires a prerequisite course of ( MATH 2300 or APPM 1360 ) and ( MATH 2001 or MATH 2002 ) (all minimum grade C-).

MATH 2300 (5) Calculus 2

Continuation of MATH 1300 . Topics include transcendental functions, methods of integration, polar coordinates, differential equations, improper integrals, infinite sequences and series, Taylor polynomials and Taylor series. Department enforced prerequisite: MATH 1300 or MATH 1310 or APPM 1345 or APPM 1350 (minimum grade C-).

Equivalent - Duplicate Degree Credit Not Granted: APPM 1360 Requisites: Requires prerequisite course of MATH 1300 or MATH 1310 or APPM 1345 or APPM 1350 (minimum grade C-).

MATH 2380 (3) Mathematics for the Environment

An interdisciplinary course where environmental issues, such as climate change, global epidemics, pollution, population models and kinship relations of Australian Aborigines are studied with elementary mathematics (such as fuzzy logic). Similar techniques are applied to analyze other current events, such as surveillance, economic meltdowns, identity theft and media literacy. Department enforced prerequisite: proficiency in high school mathematics.

MATH 2400 (5) Calculus 3

Continuation of MATH 2300 . Topics include vectors, three-dimensional analytic geometry, partial differentiation and multiple integrals, and vector analysis. Department enforced prerequisite: MATH 2300 or APPM 1360 (minimum grade C-).

Equivalent - Duplicate Degree Credit Not Granted: APPM 2350 Requisites: Requires prerequisite course of MATH 2300 or APPM 1360 (minimum grade C-).

MATH 2510 (3) Introduction to Statistics

Elementary statistical measures. Introduces statistical distributions, statistical inference, hypothesis testing and linear regression. Department enforced prerequisite: two years of high school algebra.

Additional Information: Arts Sci Core Curr: Quant Reasn Mathmat Skills Arts Sci Gen Ed: Quantitative Reasoning Math MAPS Course: Mathematics

MATH 3001 (3) Analysis 1

Provides a rigorous treatment of the basic results from elementary Calculus. Topics include the topology of the real line, sequences of numbers, continuous functions, differentiable functions and the Riemann integral.

Requisites: Requires prerequisite courses of ( MATH 2001 or MATH 2002 ) and ( MATH 2130 or MATH 3130 or MATH 2135 or MATH 3135 ) (all minimum grade C-).

MATH 3110 (3) Introduction to Theory of Numbers

Studies the set of integers, focusing on divisibility, congruences, arithmetic functions, sums of squares, quadratic residues and reciprocity, and elementary results on distributions of primes.

Requisites: Requires prerequisite of MATH 2001 or MATH 2002 (both minimum grade C-).

MATH 3120 (3) Functions and Modeling

Engages the students in daily projects and occasional in-class labs designed to strengthen and expand knowledge of the topics in secondary mathematics, focusing especially on topics from algebra, precalculus and calculus. Projects and labs involve the use of multiple representations, transformations, data analysis techniques and interconnections among ideas from geometry, algebra, probability and calculus.

MATH 3130 (3) Introduction to Linear Algebra

Equivalent - Duplicate Degree Credit Not Granted: MATH 3135 or APPM 3310 Requisites: Requires prerequisite course of MATH 2300 or APPM 1360 (minimum grade C-).

MATH 3135 (3) Honors Introduction to Linear Algebra

Equivalent - Duplicate Degree Credit Not Granted: MATH 3130 or APPM 3310 Requisites: Requires a prerequisite course of MATH 2300 or APPM 1360 and MATH 2001 (all minimum grade C-).

MATH 3140 (3) Abstract Algebra 1

Studies basic properties of algebraic structures with a heavy emphasis on groups. Other topics, time permitting, may include rings and fields.

MATH 3170 (3) Combinatorics 1

Covers basic methods and results in combinatorial theory. Includes enumeration methods, elementary properties of functions and relations, and graph theory. Emphasizes applications.

MATH 3210 (3) Euclidean and Non-Euclidean Geometry

Axiomatic systems; Euclid's presentation of the elements of geometry; Hilbert's axioms; neutral, Euclidean and non-Euclidean geometries and their models.

MATH 3430 (3) Ordinary Differential Equations

Involves an elementary systematic introduction to first-order scalar differential equations, nth order linear differential equations, and n-dimensional linear systems of first-order differential equations. Additional topics are chosen from equations with regular singular points, Laplace transforms, phase plane techniques, basic existence and uniqueness and numerical solutions. Formerly MATH 4430.

Requisites: Requires prerequisite courses of ( MATH 2400 or APPM 2350 ) and ( MATH 2130 or 3130 or MATH 2135 or 3135 or APPM 3310 ) (all minimum grade C-).

MATH 3450 (3) Introduction to Complex Variables

Theory of functions of one complex variable, including integrals, power series, residues, conformal mapping, and special functions. Formerly MATH 4450.

Requisites: Requires prerequisite courses of MATH 2400 or APPM 2350 (minimum grade C-).

MATH 3510 (3) Introduction to Probability and Statistics

Introduces the basic notions of Probability: random variables, expectation, conditioning, and the standard distributions (Binomial, Poisson, Exponential, Normal). This course also covers the Law of Large Numbers and Central Limit Theorem as they apply to statistical questions: sampling from a random distribution, estimation, and hypothesis testing.

Equivalent - Duplicate Degree Credit Not Granted: MATH 2510 or MATH 4510 Requisites: Requires a prerequisite course of ( MATH 2300 or APPM 1360 ) and ( MATH 2001 or MATH 2002 ) (all minimum grade C-).

MATH 3850 (1) Seminar in Guided Mathematics Instruction

Provides learning assistants with an opportunity to analyze assessment data for formative purposes and develop instructional plans as a result of these analyses. These formative assessment analyses will build on the literature in the learning sciences. Students gain direct experiences interacting with the tools of the trade, especially with actual assessment data and models of instruction. Restricted to learning assistants in Math.

Repeatable: Repeatable for up to 3.00 total credit hours. Requisites: Requires a corequisite course of EDUC 4610 .

MATH 4000 (3) Foundations of Mathematics

Focuses on a complete deductive framework for mathematics and applies it to various areas. Presents Goedel's famous incompleteness theorem about the inherent limitations of mathematical systems. Uses idealized computers to investigate the capabilities and limitations of human and machine computation.

Equivalent - Duplicate Degree Credit Not Granted: MATH 5000 Requisites: Requires prerequisite courses of MATH 3001 or MATH 3140 or MATH 4730 (all minimum grade C-). Additional Information: Arts Sci Gen Ed: Distribution-Arts Humanities

MATH 4001 (3) Analysis 2

Provides a rigorous treatment of infinite series, sequences of functions and an additional topic chosen by the instructor (for example, multivariable analysis, the Lebesgue integral or Fourier analysis).

Equivalent - Duplicate Degree Credit Not Granted: MATH 5001 Requisites: Requires prerequisite course of MATH 3001 (minimum grade C-).

MATH 4120 (3) Introduction to Operations Research

Studies linear and nonlinear programming, the simplex method, duality, sensitivity, transportation and network flow problems, some constrained and unconstrained optimization theory, and the Kuhn-Tucker conditions, as time permits.

Equivalent - Duplicate Degree Credit Not Granted: APPM 5120 and APPM 4120 and MATH 5120 Requisites: Requires prerequisite course of MATH 2130 or 3130 or MATH 2135 or 3135 or APPM 3310 (minimum grade C-). Additional Information: Arts Sci Gen Ed: Distribution-Natural Sciences

MATH 4140 (3) Abstract Algebra 2

Explores some topic that builds on material in MATH 3140 . Possible topics include (but are not limited to) Galois theory, representation theory, advanced linear algebra or commutative algebra.

Equivalent - Duplicate Degree Credit Not Granted: MATH 5140 Requisites: Requires prerequisite course of MATH 3140 (minimum grade C-).

MATH 4200 (3) Introduction to Topology

Introduces the basic concepts of point set topology. Includes topological spaces, metric spaces, homeomorphisms, connectedness and compactness.

Equivalent - Duplicate Degree Credit Not Granted: MATH 5200 Requisites: Requires prerequisite course of MATH 3001 (minimum grade C-).

MATH 4230 (3) Differential Geometry of Curves and Surfaces

Introduces the modern differential geometry of plane curves, space curves, and surfaces in 3-dimensional space. Topics include the Frenet frame, curvature and torsion for space curves; Gauss and mean curvature for surfaces; Gauss and Codazzi equations, and the Gauss-Bonnet theorem.

Equivalent - Duplicate Degree Credit Not Granted: MATH 5230 Requisites: Requires prerequisite courses of ( MATH 2400 or APPM 2350 ) and ( MATH 2001 or 2002 ) and ( MATH 2130 or MATH 3130 or MATH 2135 or MATH 3135 ) (all minimum grade C-).

MATH 4240 (3) Hilbert Spaces and the Mathematics of Quantum Mechanics

Provides an introduction to Hilbert spaces and their application in quantum mechanics. The primary goal is to prove and understand the so-called spectral theorem, which is crucial for the formulation of quantum mechanics. In addition, some examples from physics will be discussed, such as the quantum harmonic oscillator and the spectrum of the hydrogen atom.

Equivalent - Duplicate Degree Credit Not Granted: MATH 5240 Requisites: Requires prerequisite course of MATH 3001 (minimum grade C-). Additional Information: Arts Sci Gen Ed: Distribution-Natural Sciences

MATH 4330 (3) Fourier Analysis

The notion of Fourier analysis, via series and integrals, of periodic and nonperiodic phenomena is central to many areas of mathematics. Develops the Fourier theory in depth and considers such special topics and applications as wavelets, Fast Fourier Transforms, seismology, digital signal processing, differential equations, and Fourier optics.

Equivalent - Duplicate Degree Credit Not Granted: MATH 5330 Requisites: Requires prerequisite course of MATH 3001 (minimum grade C-). Additional Information: Arts Sci Gen Ed: Distribution-Natural Sciences

MATH 4440 (3) Mathematics of Coding and Cryptography

Gives an introduction, with proofs, to the algebra and number theory used in coding and cryptography. Basic problems of coding and cryptography are discussed.

Equivalent - Duplicate Degree Credit Not Granted: MATH 5440 Requisites: Requires prerequisite course of MATH 2130 or 3130 or MATH 2135 or 3135 (minimum grade C-).

MATH 4470 (3) Partial Differential Equations

Studies initial, boundary, and eigenvalue problems for the wave, heat, and potential equations. Solution by separation of variables, Green's function, and variational methods.

Equivalent - Duplicate Degree Credit Not Granted: MATH 5470 Requisites: Requires prerequisite courses of MATH 3430 (minimum grade C-).

MATH 4510 (3) Introduction to Probability Theory

Studies axioms, combinatorial analysis, independence and conditional probability, discrete and absolutely continuous distributions, expectation and distribution of functions of random variables, laws of large numbers, central limit theorems, and simple Markov chains if time permits.

Equivalent - Duplicate Degree Credit Not Granted: APPM 3570 or ECEN 3810 or MATH 3510 MATH 5510 Requisites: Requires prerequisite courses of ( MATH 2400 or APPM 2350 ) and ( MATH 2130 or 3130 or MATH 2135 or 3135 ) (all minimum grade C-).

MATH 4520 (3) Introduction to Mathematical Statistics

Equivalent - Duplicate Degree Credit Not Granted: MATH 5520 and STAT 4520 and STAT 5520 Requisites: Requires prerequisite course of MATH 4510 or APPM 3570 (minimum grade C-). Additional Information: Arts Sci Gen Ed: Distribution-Natural Sciences

MATH 4530 (3) Theoretical Foundations of Data Science

Introduces theoretical concepts from mathematics, statistics, and computer science required to understand and analyze data. Topics include randomized algorithms, machine learning, streaming, sketching, clustering, random matrices and graphs, graphical models and compressed sensing.

Requisites: Requires prerequisite courses of ( MATH 2130 or MATH 2135 ) and MATH 4510 (minimum grade C-).

MATH 4540 (3) Introduction to Time Series

Studies basic properties, trend-based models, seasonal models, modeling and forecasting with ARIMA models, spectral analysis and frequency filtration.

Equivalent - Duplicate Degree Credit Not Granted: MATH 5540 and STAT 4540 and STAT 5540 Requisites: Requires prerequisite course of MATH 4520 or APPM 4520 (minimum grade C-). Additional Information: Arts Sci Gen Ed: Distribution-Natural Sciences

MATH 4650 (3) Intermediate Numerical Analysis 1

Focuses on numerical solution of nonlinear equations, interpolation, methods in numerical integration, numerical solution of linear systems, and matrix eigenvalue problems. Stresses significant computer applications and software. Department enforced prerequisite: knowledge of a programming language.

Equivalent - Duplicate Degree Credit Not Granted: APPM 4650 Requisites: Requires a prerequisite course of MATH 3430 or APPM 2360 and APPM 3310 (minimum grade C-).

MATH 4730 (3) Set Theory

Studies in detail the theory of cardinal and ordinal numbers, definition by recursion, the statement of the continuum hypothesis, simple cardinal arithmetic and other topics chosen by the instructor.

Equivalent - Duplicate Degree Credit Not Granted: MATH 5730 Requisites: Requires prerequisite courses of MATH 3001 or MATH 3110 or MATH 3140 or MATH 3170 or MATH 3210 or MATH 3510 or MATH 4230 (all minimum grade C-).

MATH 4805 (1) Mathematical Teacher Training: Inclusive Pedagogy

Designed to train students to teach mathematics in an inclusive, multicultural environment. Students teach a math course within the McNeill Academic Program (Student Academic Services Center) meeting weekly with faculty and colleagues to learn to re-design curriculum, fine-tune pedagogical practices, create assessments, mentor undergraduate instructor assistants and create an inclusive classroom environment. Department enforced restriction: experience with college-level instruction.

Repeatable: Repeatable for up to 4.00 total credit hours. Requisites: Restricted to students with 87-180 credits (Seniors) or graduate students only.

MATH 4810 (1-3) Special Topics in Mathematics

Covers various topics not normally covered in the curriculum. Offered intermittently depending on student demand and availability of instructors.

Equivalent - Duplicate Degree Credit Not Granted: MATH 5810 Repeatable: Repeatable for up to 7.00 total credit hours.

MATH 4820 (3) History of Mathematical Ideas

Examines the evolution of a few mathematical concepts (e.g., number, geometric continuum, or proof), with an emphasis on the controversies surrounding these concepts. Begins with Ancient Greek mathematics and traces the development of mathematical concepts through the middle ages into the present.

Equivalent - Duplicate Degree Credit Not Granted: MATH 5820 Requisites: Prerequisite courses of MATH 2001 or MATH 2002 and one of the following: MATH 3001 , 3110 , 3120 , 3140 , 3170 , 3210 , 3430 , 3450 , 3510 , 3850 , 4000 , 4001 , 4120 , 4140 , 4200 , 4230 , 4330 , 4440 , 4510 , 4520 , 4540 , 4650 , or 4660 (all min grade C-). Recommended: completion of upper division Written Communication requirement. Additional Information: Arts Sci Gen Ed: Distribution-Arts Humanities

MATH 4890 (1-3) Honors Independent Study

Offered for students doing a thesis for departmental honors.

Additional Information: Arts Sciences Honors Course

MATH 4900 (1-3) Independent Study

Repeatable: Repeatable for up to 6.00 total credit hours.

MATH 5000 (3) Foundations of Mathematics

Equivalent - Duplicate Degree Credit Not Granted: MATH 4000 Requisites: Restricted to graduate students only.

MATH 5001 (3) Analysis 2

Equivalent - Duplicate Degree Credit Not Granted: MATH 4001 Requisites: Restricted to graduate students only.

MATH 5030 (3) Intermediate Mathematical Physics 1

Surveys classical mathematical physics, starting with complex variable theory and finite dimensional vector spaces. Discusses topics in ordinary and partial differential equations, the special functions, boundary value problems, potential theory, and Fourier analysis. Department enforced prerequisite: MATH 4001 . Instructor consent required for undergraduates.

Equivalent - Duplicate Degree Credit Not Granted: PHYS 5030 Requisites: Restricted to graduate students only.

MATH 5040 (3) Intermediate Mathematical Physics 2

Surveys classical mathematical physics, starting with complex variable theory and finite dimensional vector spaces. Discusses topics in ordinary and partial differential equations, the special functions, boundary value problems, potential theory and Fourier analysis. Department enforced prerequisite: MATH 5030 .

Equivalent - Duplicate Degree Credit Not Granted: PHYS 5040 Requisites: Restricted to graduate students only.

MATH 5120 (3) Introduction to Operations Research

Equivalent - Duplicate Degree Credit Not Granted: APPM 4120 and MATH 4120 and APPM 5120 Requisites: Restricted to graduate students only. Recommended: Prerequisites APPM 3310 OR MATH 2130 OR MATH 2135 or equivalent.

MATH 5140 (3) Abstract Algebra 2

Explores some topic that builds on material in MATH 3140 . Possible topics include (but are not limited to) Galois theory, representation theory, advanced linear algebra or commutative algebra. Department enforced prerequisite: MATH 3140 .

Equivalent - Duplicate Degree Credit Not Granted: MATH 4140 Requisites: Restricted to graduate students only.

MATH 5150 (3) Linear Algebra

Highlights vector spaces, linear transformations, eigenvalues and eigenvectors, and canonical forms. Department enforced prerequisite: MATH 2130 or MATH 2135 . Instructor consent required for undergraduates.

Requisites: Restricted to graduate students only.

MATH 5200 (3) Introduction to Topology

Equivalent - Duplicate Degree Credit Not Granted: MATH 4200

MATH 5230 (3) Differential Geometry of Curves and Surfaces

Equivalent - Duplicate Degree Credit Not Granted: MATH 4230 Requisites: Restricted to graduate students only.

MATH 5240 (3) Hilbert Spaces and the Mathematics of Quantum Mechanics

Equivalent - Duplicate Degree Credit Not Granted: MATH 4240 Requisites: Restricted to graduate students only.

MATH 5330 (3) Fourier Analysis

Equivalent - Duplicate Degree Credit Not Granted: MATH 4330 Requisites: Restricted to graduate students only.

MATH 5430 (3) Ordinary Differential Equations

Introduces theory and applications of ordinary differential equations, including existence and uniqueness theorems, qualitative behavior, series solutions, and numerical methods, for scalar equations and systems. Department enforced prerequisites: MATH 2130 and MATH 3001 . Instructor consent required for undergraduates.

MATH 5440 (3) Mathematics of Coding and Cryptography

Gives an introduction, with proofs, to the algebra and number theory used in coding and cryptography. Basic problems of coding and cryptography are discussed; prepares students for the more advanced ECEN 5682 .

Equivalent - Duplicate Degree Credit Not Granted: MATH 4440 Requisites: Restricted to graduate students only.

MATH 5470 (3) Partial Differential Equations

Studies initial boundary and eigenvalue problems for the wave, heat and potential equations. Solution by separation of variables, Green's function, and variational methods. Department enforced prerequisite: MATH 3430 or MATH 5430 . Instructor consent required for undergraduates.

Equivalent - Duplicate Degree Credit Not Granted: MATH 4470 Requisites: Restricted to graduate students only.

MATH 5510 (3) Introduction to Probability Theory

Equivalent - Duplicate Degree Credit Not Granted: MATH 4510 Requisites: Restricted to graduate students only.

MATH 5520 (3) Introduction to Mathematical Statistics

Examines point and confidence interval estimation. Principles of maximum likelihood, sufficiency, and completeness: tests of simple and composite hypotheses, linear models, and multiple regression analysis if time permits. Analyzes various distribution-free methods. Department enforced prerequisite: one semester calculus-based probability course, such as MATH 4510 or APPM 3570 .

Equivalent - Duplicate Degree Credit Not Granted: STAT 4520 and MATH 4520 and STAT 5520 Requisites: Restricted to graduate students only. Recommended: Prerequisite previous coursework equivalent to APPM 3570 or STAT 3100 or MATH 4510 ; minimum grade of C- for all.

MATH 5540 (3) Introduction to Time Series

Studies basic properties, trend-based models, seasonal models modeling and forecasting with ARIMA models, spectral analysis and frequency filtration. Department enforced prerequisite: APPM 5520 or MATH 5520 .

Equivalent - Duplicate Degree Credit Not Granted: STAT 4540 and MATH 4540 and STAT 5540 Requisites: Restricted to graduate students only.

MATH 5600 (3) Numerical Analysis 1

Solution of nonlinear algebraic equations, interpolation, approximation theory and numerical integration. Department enforced prerequisites: MATH 2130 or MATH 2135 or APPM 3310 and experience with a scientific programming language. Instructor consent required for undergraduates.

MATH 5610 (3) Numerical Analysis 2

Solution of linear systems, eigenvalue problems, optimization problems, and ordinary and partial differential equations. Department enforced prerequisite: MATH 5600 or APPM 5600 . Instructor consent required for undergraduates.

MATH 5730 (3) Set Theory

Equivalent - Duplicate Degree Credit Not Granted: MATH 4730

MATH 5810 (1-3) Special Topics in Mathematics

Equivalent - Duplicate Degree Credit Not Granted: MATH 4810 Repeatable: Repeatable for up to 7.00 total credit hours. Requisites: Restricted to graduate students only.

MATH 5820 (3) History of Mathematical Ideas

Equivalent - Duplicate Degree Credit Not Granted: MATH 4820 Requisites: Restricted to graduate students only. Recommended: Requisite completion of upper division Written Communication requirement.

MATH 5905 (1) Mathematics Teacher Training

Designed to train students to become effective teachers. Students teach a mathematics course, meeting weekly with faculty to discuss problems particular to the teaching of mathematics. Department enforced prerequisite: current employment as a teaching assistant.

MATH 6000 (3) Model Theory

Proves the compactness theorem, showing the essential finiteness of logical implication. Proves many basic properties of theories, showing how the syntactic form of statements influences their behavior w.r.t., different models. Finally, studies properties of elements that cannot be stated by a single formula (the type of the element) and shows it can be used to characterize certain models.

MATH 6010 (3) Computability Theory

Studies the computable and uncomputable. Shows that there are undecidable problems and from there builds up the theory of sets of natural numbers under Turing reducibility. Studies Turing reducibility, the arithmetical hierarchy, oracle constructions and end with the finite injury priority method. Department enforced prerequisite: MATH 6000 .

MATH 6020 (3) Category Theory

Studies categories, functors, natural transformations, adjoints, and universal constructions. Special topics may include monads and their algebras, abelian categories, Kan extensions, or sheaves in geometry and logic. Instructor consent required for undergraduates.

MATH 6110 (3) Introduction to Number Theory

Examines divisibility properties of integers, congruences, diophantine equations, arithmetic functions, quadratic residues, distribution of primes and algebraic number fields. Department enforced prerequisite: MATH 3140 . Instructor consent required for undergraduates.

MATH 6130 (3) Algebra 1

Studies group theory and ring theory. Department enforced prerequisite: MATH 3140 . Instructor consent required for undergraduates.

MATH 6140 (3) Algebra 2

Studies modules, fields and Galois theory. Department enforced prerequisite: MATH 6130 . Instructor consent required for undergraduates.

MATH 6150 (3) Commutative Algebra

Introduces topics used in number theory and algebraic geometry, including radicals of ideals, exact sequences of modules, tensor products, Ext, Tor, localization, primary decomposition of ideals and Noetherian rings. Department enforced prerequisite: MATH 6140 . Instructor consent required for undergraduates.

MATH 6170 (3) Algebraic Geometry

Introduces algebraic geometry, including affine and projective varieties, rational maps and morphisms and differentials and divisors. Additional topics might include Bezout's Theorem, the Riemann-Roch Theorem, elliptic curves, and sheaves and schemes. Department enforced prerequisite: MATH 6140 . Instructor consent required for undergraduates.

MATH 6175 (3) Algebraic Geometry 2

Continuation of MATH 6170 . Develops algebraic geometry using schemes. Topics include coherent and quasicoherent sheaves, sheaf cohomology, Serre duality, lifting criteria, smoothness, base change theorems, algebraic curves and surfaces, and additional topics at the discretion of the instructor. Instructor consent required for undergraduates. Department enforced prerequisite: MATH 6170 .

Requisites: Restricted to graduate students only. Recommended: Prerequisites MATH 6150 or MATH 6290 .

MATH 6180 (3) Algebraic Number Theory

Introduces number fields and completions, norms, discriminants and differents, finiteness of the ideal class group, Dirichlet's unit theorem, decomposition of prime ideals in extension fields, decomposition and ramification groups. Department enforced prerequisites: MATH 6110 and MATH 6140 . Instructor consent required for undergraduates.

MATH 6190 (3) Analytic Number Theory

Acquaints students with the Riemann Zeta-function and its meromorphic continuation, characters and Dirichlet series, Dirichlet's theorem on primes in arithmetic progressions, zero-free regions of the zeta function and the prime number theorem. Department enforced prerequisites: MATH 6110 and MATH 6350 . Instructor consent required for undergraduates.

MATH 6210 (3) Introduction to Topology 1

Introduces elements of point-set topology and algebraic topology, including the fundamental group and elements of homology. Department enforced prerequisites: MATH 2130 and MATH 3140 and MATH 4001 . Instructor consent required for undergraduates.

MATH 6220 (3) Introduction to Topology 2

Continuation of MATH 6210 . Department enforced prerequisite: MATH 6210 . Instructor consent required for undergraduates.

MATH 6230 (3) Introduction to Differential Geometry 1

Introduces topological and differential manifolds, vector bundles, differential forms, de Rham cohomology, integration, Riemannian metrics, connections and curvature. Department enforced prerequisites: MATH 2130 and MATH 4001 . Instructor consent required for undergraduates.

MATH 6240 (3) Introduction to Differential Geometry 2

Continuation of MATH 6230 . Department enforced prerequisite: MATH 6230 . Instructor consent required for undergraduates.

MATH 6250 (3) Theory of Rings

Studies semi-simple Artinian rings, the Jacobson radical, group rings, representations of finite groups, central simple algebras, division rings and the Brauer group. Department enforced prerequisites: MATH 6130 and MATH 6140 . Instructor consent required for undergraduates.

MATH 6260 (3) Geometry of Quantum Fields and Strings

Focuses on differential geometric techniques in quantum field and string theories. Topics include: spinors, Dirac operators, index theorem, anomalies, geometry of superspace, supersymmetric quantum mechanics and field theory and nonperturbative aspects in field and string theories. Department enforced prerequisites: MATH 6230 and MATH 6240 and PHYS 5250 and PHYS 7280 . Instructor consent required for undergraduates.

Equivalent - Duplicate Degree Credit Not Granted: PHYS 6260 Requisites: Restricted to graduate students only.

MATH 6270 (3) Theory of Groups

Studies nilpotent and solvable groups, simple linear groups, multiply transitive groups, extensions and cohomology, representations and character theory, and the transfer and its applications. Department enforced prerequisites: MATH 6130 and MATH 6140 . Instructor consent required for undergraduates.

MATH 6280 (3) Advanced Algebraic Topology

Covers homotopy theory, spectral sequences, vector bundles, characteristic classes, K-theory and applications to geometry and physics. Department enforced prerequisite: MATH 6220 . Instructor consent required for undergraduates.

MATH 6290 (3) Homological Algebra

Studies categories and functors, abelian categories, chain complexes, derived functors, Tor and Ext, homological dimension, group homology and cohomology. If time permits, the instructor may choose to cover additional topics such as spectral sequences or Lie algebra homology and cohomology. Department enforced prerequisites: MATH 6130 and MATH 6140 .

MATH 6310 (3) Introduction to Real Analysis 1

Develops the theory of Lebesgue measure and the Lebesgue integral on the line, emphasizing the various notions of convergence and the standard convergence theorems. Applications are made to the classical L^p spaces. Department enforced prerequisite: MATH 4001 . Instructor consent required for undergraduates.

MATH 6320 (3) Introduction to Real Analysis 2

Covers general metric spaces, the Baire Category Theorem, and general measure theory, including the Radon-Nikodym and Fubini theorems. Presents the general theory of differentiation on the real line and the Fundamental Theorem of Lebesgue Calculus. Instructor consent required for undergraduates.

Requisites: Restricted to graduate students only. Recommended: Prerequisite MATH 6310 .

MATH 6350 (3) Functions of a Complex Variable 1

Focuses on complex numbers and the complex plane. Includes Cauchy-Riemann equations, complex integration, Cauchy integral theory, infinite series and products, and residue theory. Department enforced prerequisite: MATH 4001 . Instructor consent required for undergraduates.

MATH 6360 (3) Functions of a Complex Variable 2

Focuses on conformal mapping, analytic continuation, singularities and elementary special functions. Department enforced prerequisite: MATH 6350 . Instructor consent required for undergraduates.

MATH 6534 (3) Topics in Mathematical Probability

Offers selected topics in probability such as sums of independent random variables, notions of convergence, characteristic functions, Central Limit Theorem, random walk, conditioning and martingales, Markov chains and Brownian motion. Department enforced prerequisite: MATH 6310 . Instructor consent required for undergraduates

MATH 6550 (3) Introduction to Stochastic Processes

Systematic study of Markov chains and some of the simpler Markov processes, including renewal theory, limit theorems for Markov chains, branching processes, queuing theory, birth and death processes, and Brownian motion. Applications to physical and biological sciences. Department enforced prerequisite: MATH 4001 or MATH 4510 or APPM 3570 or APPM 4560 . Instructor consent required for undergraduates.

Equivalent - Duplicate Degree Credit Not Granted: APPM 6550 Requisites: Restricted to graduate students only.

MATH 6730 (3) Set Theory

Presents cardinal and ordinal arithmetic, and basic combinatorial concepts, including stationary sets, generalization of Ramsey's theorem, and ultrafilters, consisting of the axiom of choice and the generalized continuum hypothesis. Department enforced prerequisites: MATH 4000 or MATH 5000 and MATH 4730 or MATH 5730 . Instructor consent required for undergraduates.

MATH 6740 (3) Forcing

Presents independence of the axiom of choice and the continuum hypothesis, Souslin's hypothesis and other applications of the method of forcing. Introduces the theory of large cardinals. Department enforced prerequisite: MATH 6730 . Instructor consent required for undergraduates.

MATH 6900 (1-3) Independent Study

Instructor consent required for undergraduates.

Repeatable: Repeatable for up to 6.00 total credit hours. Requisites: Restricted to graduate students only.

MATH 6940 (1) Master's Candidate for Degree

This course is for students preparing for the no-thesis option for a master's degree. The content is set by the students' advisors.

MATH 6950 (1-6) Master's Thesis

MATH 8114 (3) Topics in Number Theory

May include the theory of automorphic forms, elliptic curves, or any of a variety of advanced topics in analytic and algebraic number theory. Department enforced prerequisite: MATH 6110 . Instructor consent required for undergraduates.

MATH 8174 (3) Topics in Algebra I

Department enforced prerequisites: MATH 6130 and MATH 6140 . Instructor consent required for undergraduates.

MATH 8234 (3) Topics in Differential Geometry

Presents advanced topics in Differential Geometry, such as index theory, partial differential equations on manifolds, exterior differential systems, and Cartan's methods.

Repeatable: Repeatable for up to 12.00 total credit hours. Allows multiple enrollment in term. Requisites: Requires prerequisite courses of MATH 6230 and MATH 6310 (minimum grade D-). Restricted to graduate students only. Instructor consent required for undergraduates.

MATH 8250 (3) Mathematical Theory of Relativity 1

Focuses on Maxwell equations, Lorentz force, Minkowski space-time, Lorentz, Poincare, and conformal groups,metric manifolds, covariant differentiation, Einstein space-time, cosmologies, and unified field theories. Instructor consent required.

MATH 8304 (3) Topics in Analysis 1

Presents advanced topics in analysis including Lie groups, Banach algebras, operator theory, ergodic theory, representation theory, etc. Department enforced prerequisites: MATH 8330 and MATH 8340 . Instructor consent required for undergraduates.

MATH 8330 (3) Functional Analysis 1

Introduces such topics as Banach spaces (Hahn-Banach theorem, open mapping theorem, etc.), operator theory (compact operators and integral equations and spectral theorem for bounded self-adjoint operators) and Banach algebras (the Gelfand theory). Department enforced prerequisites: MATH 6310 and MATH 6320 . Instructor consent required for undergraduates. See also MATH 8340 .

MATH 8340 (3) Functional Analysis 2

Introduces such topics as Banach spaces (Hahn-Banach theorem, open mapping theorem, etc.), operator theory (compact operators and integral equations and spectral theorem for bounded self-adjoint operators) and Banach algebras (the Gelfand theory). Department enforced prerequisite: MATH 8330 . Instructor consent required for undergraduates. See also MATH 8330 .

MATH 8370 (3) Harmonic Analysis 1

Examines trigonometric series, periodic functions, diophantine approximation and Fourier series. Also covers Bohr and Stepanoff almost periodic functions, positive definite functions and the L^1 and L^2 theory of the Fourier integral. Applications to group theory and differential equations. Department enforced prerequisites: MATH 5150 and MATH 6320 . Instructor consent required for undergraduates.

MATH 8714 (3) Topics in Logic 1 and 2

MATH 8815 (1-3) Ulam Seminar

Repeatable: Repeatable for up to 3.00 total credit hours. Allows multiple enrollment in term. Requisites: Restricted to graduate students only.

MATH 8900 (1-3) Independent Study

MATH 8990 (1-10) Doctoral Dissertation

All doctoral students must register for not fewer than 30 hours of dissertation credit as part of the requirements for the degree. For a detailed discussion of doctoral dissertation credit, refer to the Graduate School portion of the catalog.

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Bachelor of Science in Applied Computer Science Post-Baccalaureate

Our online Bachelor of Science in Applied Computer Science Post-Baccalaureate degree is designed for working professionals with a prior bachelor’s degree who are looking to make a career pivot, move ahead in their current career path, or deepen their knowledge of computer science in 45 credits. The program’s flexible format allows you to pursue your degree, full-time or part-time, from anywhere in the world.

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Graduate Program
Request Graduate Information. Thank you for your interest in the graduate program in Mathematics at the University of Colorado Boulder.We offer doctor of philosophy (PhD) and master of arts (MA) degrees in mathematics, as well as a master of science (MS) degree. We have an award-winning graduate faculty of 27, with current areas of research ...
Any math PhD's here? : r/cuboulder
Since MATH is in the college of arts and science with a very high undergrad acceptance rate (over 80%), you will get lots of students with poor math background who don't want to be there. Moreover, the fact that APPM (applied math) calculus has the reputation to be harder than MATH exacerbates this problem, as more unmotivated students self ...
Applied Mathematics
A minimum of 60 credits is required for the degree, including 30 credits in courses numbered 5000 or above ( APPM 5350 , APPM 5360, STAT 5000 and APPM 5720 generally do not count toward this requirement) and 30 credits of applied math dissertation credit. A grade of B - or higher must be attained in each course.
University of Colorado—Boulder
Acceptance Rate: 81%. Tuition (In-State): $11,520. SAT Scores (EBRW + Math): 1150 - 1390. ... CU Boulder also offers a "strong environmental program" with opportunities for "both onand off-campus" study. Students say the professors are "amazing," "approachable," "interested in students personally," and "will treat you as ...
University of Colorado Boulder Admissions
CU Boulder admissions is somewhat selective with an acceptance rate of 80%. Students that get into CU Boulder have an average SAT score between 1170-1390 or an average ACT score of 25-31. The regular admissions application deadline for CU Boulder is January 15. Interested students can apply for early action, and the CU Boulder early action ...
University of Colorado Boulder Acceptance Rates & Admissions Statistics
Average Test Scores. About 32% of students accepted to CU - Boulder submitted their SAT scores. When looking at the 25th through the 75th percentile, SAT Evidence-Based Reading and Writing scores ranged between 590 and 690. Math scores were between 580 and 700. SAT Reading and Writing Scores for University of Colorado Boulder ( 590 to 690 ) 200.
University of Colorado--Boulder
Campus Box 395, Boulder, CO 80309-0395 (303) 492-3161. [email protected]. Website
Mathematics
Admission Requirements. Applicants must have demonstrated mathematical maturity and accomplishment roughly at the level of a successful mathematics major at CU Boulder. Applicants must also demonstrate mathematical potential: success in courses in advanced calculus and abstract algebra help demonstrate this potential.
University of Colorado Boulder Admissions
University of Colorado Boulder admissions has an acceptance rate of 79% and an early acceptance rate of 93.7%. Half the applicants admitted to University of Colorado Boulder who submitted test ...
CU Boulder Acceptance Rate & Average GPA
The historical trend chart shows acceptance rates from the previous years, from which we have projected the acceptance rate for the 2024-2025 school year. The overall acceptance rate trend for University of Colorado Boulder has been staying about the same from year to year. Acceptance Rate By Year. 2016-2017: 76.6%; 2017-2018: 79.8%; 2018-2019: ...
Is the physics department really that good? : r/cuboulder
Yes the physics program is good, but as an undergrad it does not matter a whole lot other than access to good research opportunities. Those rankings are more related to grad programs and research. CU is home to JILA and has a very large graduate physics enrollment, 4th in the country when I graduated. 42. Reply.
Graduate School Acceptance Rates: Can You Get In?
For example, in 2016 University of Michigan's math doctoral program had a 17.2 percent acceptance rate, whereas its master's program had a much higher 31.8 percent rate. In this case, the doctoral program is clearly tougher to get into than the master's program.
Doctoral Degree Requirements < University of Colorado Boulder
PhD students must be registered as full time, regular degree-seeking students at CU Boulder, for a minimum of 5 dissertation hours during the semester in which they pass the final examination. DMA students must be registered, full-time for DMA dissertation credits (courses 8200-8399) or TMUS 8029 during the semester in which they pass the ...
Department of Mathematics
Welcome to the Mathematics Department of the University of Colorado Boulder. We have a broad range of research interests in Mathematics, including Algebraic and Differential Geometry, Combinatorics, Logic and Foundations, Mathematical Physics, Partial Differential Equations, Number Theory, Noncommutative Geometry, Operator Algebras, Probability, and Topology.
Admissions < University of Colorado Boulder
Application Procedures. Students seeking admission to a CU Boulder master's or doctoral program apply directly to the appropriate department. An applicant for admission must present complete application materials, including: the graduate application, available online at Graduate School Admissions, unofficial transcripts for all academic work ...
PhD in Applied Mathematics
Business Hours: Monday through Friday 7:30 am to 3:30 pm. Phone: 303-315-1700 Fax: 303-315-1704 Email: [email protected] Map Location
What's the acceptance rate for Boulder?
The acceptance rate for the University of Colorado Boulder in the most recent admission cycle was around 79%. Keep in mind that acceptance rates can vary from year to year, but this should give you a rough idea of the level of selectivity at CU Boulder. ... 720 math. 200. 800 | 800 verbal. 200. 800. Gender not specified. ... but this should ...
Admissions
Graduation rates and other information on Pre-collegiate Development Program (PCDP) completers who enrolled at CU Boulder, 9/2012 (PDF) Freshmen College credits already earned by entering freshmen , 1990, 1995, 2000-12 (Excel) Includes AP (Advanced Placement, with qualifying exam scores) and IB (International Baccalaureate) hours.
Mathematics (MATH) < University of Colorado Boulder
Mathematics - Doctor of Philosophy (PhD) Molecular, Cellular and Developmental Biology Toggle Molecular, Cellular and Developmental Biology. ... 1160 (minimum grade C-) or an ALEKS math exam taken in 2016 or earlier, or placement into pre-calculus based on your admission data and/or CU Boulder coursework. ...
Admissions
CU research has led to the creation of more than 190 new companies in the last 25 years. #1 public university recipient of NASA funding among public universities - and second among all universities. CU Boulder is the #1 NIH-funded non-medical school. CU Boulder ranks #8 in National Science Foundation Graduate Research Fellowship awards.
Bachelor of Science in Applied Computer Science Post-Baccalaureate
learn the algorithms and mathematics that underlie Computer Science, Data Science, Artificial Intelligence and Machine Learning, ... With a computer science degree from CU Boulder's prestigious College of Engineering and Applied Science, you'll be positioned to take advantage of one of the world's fastest-growing career fields ...

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