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Honors Mathematics

The Mathematics Honors Program provides opportunities and assistance to talented undergraduates hoping to graduate with Latin Honors in mathematics.

Eligibility

Requirements for Math majors

Senior Latin Honors thesis

One requirement for graduating with Latin honors in mathematics is to:

• Take the required thesis course (HCOL 3101H or HCOL 3102H).
• Complete an honors thesis under the supervision of a  faculty mentor .
• Summarize your thesis work in a printed scientific poster.
• Give a short public presentation of your work.
• Submit to an oral exam by your faculty committee (summa cum laude students only).

Normally students contact a faculty member who works in an area of interest. That faculty member, if willing, will suggest a topic of study, or in some cases, a topic of research that is suitable. 

Thesis guide and searchable thesis database 

Honors Math courses

+ lower division courses, math 1571h/1572h: honors calculus i/ii.

This is the introductory Honors Calculus sequence. It begins with a discussion of functions, limits, and continuity. The course then proceeds to the main topics of differentiation and integration of functions of a single real variable. One then studies the properties of these key operations, including the chain rule, the fundamental theorem of calculus, and methods of integration. Applications from the physical and biological sciences are emphasized. Applications include max-min problems, related rates, arc length, volumes, and surface area of solids of revolution. Sequences and series are also studied. The course strives to provide an introduction to the mathematical method of proof and to mathematical rigor.

MATH 2573H/2574H: Honors Calculus III/IV

This course is a two-semester course covering multivariable calculus, including differentiation of functions of several variables, multiple integration, discussion of chain rule, inverse function theorem, implicit function theorem, multiple integration, and Fubini’s theorem. Applications include max-min problems using Lagrange multipliers, volume, and surface area. The course also treats vector calculus, vector fields, div, curl, grad, Green’s theorem, Stokes’ theorem, and Gauss’ theorem. Also covered are linear algebra, including the study of eigenvalues and eigenvectors, and the application to diagonalization of suitable linear transformations. The course provides an introduction to ordinary differential equations, particularly first-order equations, constant-coefficient linear equations, variation of parameters, first-order systems, and Laplace transforms. Applications from the physical sciences will be emphasized.

MATH 3592H/3593H: Honors Mathematics I/II

This course is an Honors course designed for students who are interested in pursuing mathematics beyond basic calculus or are interested in why theorems hold and wish to understand the mathematical reasoning underlying mathematical results, or who enjoy doing mathematics for its own sake. As such, the course will help prepare students for advanced undergraduate courses and graduate courses in math. The course emphasizes mathematical proof and rigor. It is a 5-credit course and is more demanding than 2573H-4H, although both courses have a large overlap in content. While this course covers in depth the topics of multivariable calculus and linear algebra and vector calculus, it does not cover in any detail the introduction to ordinary differential equations. It is recommended that students needing or desiring this subject take an additional course (several excellent courses in ordinary differential equations are offered at the 5000 level). Some topics covered in 3592H-3H (which are not covered in 2573H-4H) include greater attention to n-variable cases (n greater than 3), manifolds, the spectral theorem for real symmetric matrices and applications to classification of real quadratic forms, applications to max-min-saddlepoint classification of critical points, differential forms on manifolds and exterior differentiation, integration on manifolds, and generalized Stokes’ theorem.

+ Upper division courses

Math 5285h/5286h - honors: fundamental structures of algebra i/ii.

This course introduces the study of basic algebraic structures, sub-objects, quotient objects, and maps between objects. In particular, groups, rings, modules, and fields are treated. Some topics covered are the Sylow theorems, factorizations in integral domains, principal ideal domains, unique factorization domains, chain conditions in commutative rings, structure theorem for finitely generated modules over a pid, applications to linear algebra (Jordan normal form), finite fields, and elementary Galois theory.

MATH 5345H - Honors: Topology

This course focuses on abstract topological spaces, both the concrete and the very formal, the non-intuitive and the geometric. Along with an emphasis on the ability to effectively communicate mathematical arguments, in this course, students will develop qualitative tools to characterize topological spaces (e.g., connectedness, compactness, second countable, Hausdorff...), develop tools to identify when two spaces are equivalent (homeomorphic), and explore examples and counter-examples that inform the development of the subject.  Several important results will be proved, such as the Tychonoff theorem on products, but an equal focus will be placed on understanding examples coming from geometry, algebra, and number theory. Other topics include the fundamental group and, if time permits, covering spaces.

MATH 5615H/5616H - Honors: Introduction to Analysis I/II

This course gives a rigorous treatment of basic analysis. It covers metric spaces, convergence, connectedness, compactness, uniform convergence of sequences, and series of functions in one and several variables. Also covered are the Stone-Weierstrass theorem, rigorous development of differentiation and Riemann-Stieltjes integration, Taylor’s theorem, Implicit function theorem, and Stokes’ theorem.

How to register: Honors Math courses

Undergraduate Mathematics Office 115 Vincent Hall

[email protected] 612-625-4848

Latin Honors Adviser

Professor Dmitriy Bilyk Latin Honors Adviser for Mathematics Majors

[email protected]

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Undergraduate Capstone Project

Types of Capstones

Students completing a capstone in anthropology may opt for either the: 

• The  In-Class Capstone , which comprises an additional 4xxx/5xxx ANTH course plus a 1-credit add-on course, ANTH 4093 .
• The  Independent Capstone Project I and II , which is a substantial independent research project that you work on over two semesters. Students in the University Honors Program are expected to choose the Independent Capstone Project I and II .  Honors students should review the information here:  Honors Capstone Requirement.

These two options are offered to meet the different interests, schedules, needs, and career goals of our majors, and deciding which option to pursue will depend on the student's individual circumstances and future plans. Below, is a brief outline of the two options and what they involve in order to help decide which of the two would best suit each student.  

Registration Deadline

Be sure to complete all steps needed for your registration before the end of the second week of the semester (fall or spring). After the second week, you will need to take additional steps to add the course to your registration. Contact the anthropology undergraduate advisor, Peter Harle ( [email protected] ), to determine what additional steps may be needed.

In-Class Capstone Project

The In-Class Capstone option is designed to allow students to complete the Capstone requirement in a single semester. Select a 4xxx/5xxx-level ANTH course (of 3 or more credits) to take in addition to the ones used for the major electives and subfield foundations requirements.

Reasons for registering for the In-Class Capstone Option

Students may decide to take this Capstone option for a variety of reasons.

• First, the In-Class option allows students to complete the course within a single semester which may be an important factor for your graduation timeline.
• Second, the In-Class option is ideal for a student who has a strong interest in the topic area of a particular upper-level class or lab and wants to do additional work in relation to that topic as part of the class.
• Third, a student may feel that they are not prepared to conduct independent research and wish to seek further training through class-based learning.
• Finally, a student may seek to study further with a particular faculty member who may not be in the position to supervise a research-based Independent Capstone with the student.

Whatever your reasons, the In-Class Capstone option will allow you to explore the topics of the class more fully in a single semester and will require some kind of work that exceeds the set syllabus. The faculty member supervising the In-Class Capstone will give you a grade both for the regular class and for the Capstone work you produce via your registration in the one-credit ANTH 4093. 

With few exceptions, all 4xxx/5xxx courses offered in the department by regular teaching faculty (that is, faculty who are not graduate instructors) will have an In-Class option for the class. The specific requirements for the In-Class option will differ from faculty member to faculty member, and from class to class. However, in most cases, the nature of the requirements will align with the requirements for the regular syllabus. Faculty should include details about the work required for fulfilling the Capstone requirement in their regular class syllabi, and you should inquire in advance about those requirements. 

While most of our regular classroom and lab 4xxx courses will be suitable for this, you must receive confirmation from the instructor that a particular course is eligible for this option as part of the registration process.

Alongside this class, you will also register for ANTH 4093.

ANTH 4093 In-Class Capstone Project

The one-credit ANTH 4093 add-on course acknowledges the additional work you will undertake in the regular 4xxx/5xxx class in order to fulfill the capstone requirement. Capstone work associated with the class is intended to provide a qualitatively different experience for capstone students than those who are taking the course for regular credit. Faculty should include details about the work required for fulfilling the ANTH 4093 requirement in the regular class syllabus.

To register for the In-Class Capstone Option:

You should register for the specific 4xxx/5xxx class you plan to use to meet this requirement as you would for any other class.

To register for the one-credit add-on course, ANTH 4093:

• Verify with the instructor that the additional 4xxx/5xxx course can be used for the In-Class Capstone option, and check the syllabus to be sure that you understand the additional requirements for the capstone.
• Ask the instructor to confirm by email that you can take this class to satisfy the In-Class Capstone Project.
• Forward the confirmation email from the instructor to the departmental administrator, Taryn Varley ( [email protected] ), who will then give you a permission number that will allow you to register for ANTH 4093.

Independent Capstone Project I and II

The Independent Capstone Project I (ANTH 3993) and II (ANTH 4013 or 4013H) is designed to allow students to carry out a major independent research project in a two-semester sequence. This option will require you, in collaboration with a faculty mentor, to develop a research idea and project design, to gather primary data (either through an experiment, quantitative observations, or ethnographic study), and produce a written thesis (or a similar product, such as a documentary film) that engages your data, findings, and conclusions.

Preparation: Identifying a Research Project and Selecting a Faculty Mentor

In the semester prior to registering for ANTH 3993 you will need to identify a faculty member whose research interests and methods align with your research questions, and whose schedule allows them to supervise your research and thesis. You do not need to have a specific plan or question in advance of approaching a faculty member, but you should minimally have an idea of the subfield, topical area, and some sense of what broad questions intrigue you. Conversations with faculty will help you refine your questions and develop a project that has achievable parameters and that can be scaled to the timeline of the Capstone project. Often, students approach faculty they have taken classes with and whose research interests, topical or geographic areas of expertise, or ongoing research projects align with the student’s, but that is not essential.  Faculty research interests are outlined on the departmental website.  

In ANTH 3993 (1 credit):  Ideally you will carry out the bulk of your primary research (see more below). The specific requirements for this class will be negotiated between you and your faculty mentor. A typical Independent Capstone Project I will consist of meetings every 2-3 weeks and result in an annotated bibliography, project proposal, ethics review process (if necessary), and the primary research for the project. 

However, because the timeline of primary research depends on many factors and constraints (field site availability, the timing of excavations, travel plans, study abroad schedules, mentors’ schedules, pre-planned lab projects, unanticipated results, and more), realistically the work of ANTH 3993 extends beyond the formal registration period, as explained below.

While this is formally a two-semester option, the preparation for the Independent Capstone should start the semester prior to registration for ANTH 3993,  which is why you need to be planning for your Capstone in your junior year if you intend to take this option .  All primary research projects have uneven timelines, so it is not always possible to contain a research project into the nine months of an academic year. In addition, a single semester is often not long enough to complete primary research, nor may it align with a field research opportunity (e.g. a study abroad semester, a field research season, or a faculty member’s summer lab-based research that your Capstone research draws on). As such, students frequently do a significant amount of the actual primary research in the summer prior to or after registration for ANTH 3993. For example, for students registered for ANTH 3993 in the spring, research planning and design, bibliographic research, ethics review, and identifying sites may take up much of the semester while the actual primary research may take place in the summer. For students registering for ANTH 3993 in the fall, planning informally with the faculty mentor in the prior spring (and having your proposal reviewed by the university’s ethics review board, if necessary) may still allow the student to conduct significant research in the summer and complete more of the bibliographic research and analysis of data in the fall semester when registered for ANTH 3993. 

Here are a few examples, based on prior student experiences to give you a sense of how timelines and the specific demands of research opportunities may shape your decisions:

• You know you intend to study abroad in the fall semester of your senior year and wish to conduct research in the location where you will be based around a topic you have identified. In the fall semester of your junior year, you approach a faculty member who agrees to supervise your project. In the spring of your junior year while still in Minnesota, you register for ANTH 3993 and with your mentor’s help begin to refine your research questions, identify key bibliographic sources, and go through ethics review because you will be conducting research with human subjects. You spend your summer reading and refining your project but conduct your actual research in the fall when you are studying abroad and when it would not be possible to register for ANTH 3993 without incurring additional registration costs. In the spring of your senior year, after your return, you register for the Independent Capstone II (ANTH 4013/H).
• While taking a lab-based course with a faculty member in the fall semester of your junior year, you find out about the faculty member’s plans for summer research in their lab that interests you. You ask the faculty member if there is a part of their research you could contribute to, and they suggest an independent project that algins with their own project. You register for ANTH 3993 in the spring of your junior year, planning the research with the faculty member, getting involved in the set-up for the summer research and continuing the research through the summer so that you can register for ANTH 4013/H in the fall semester of your senior year. 
• You are interested in conducting ethnographic research in a community you are part of in the Twin Cities area and can conduct it at any time, but the best time to participate in and observe this community is in late spring, going into the summer. It would make most sense to register for ANTH 3993 in the spring of your junior year so your planning can coincide with the timeline of the community you plan to study and do the bulk of the research in the summer, allowing you to register for ANTH 4013/H in the fall semester of your senior year.
• In all cases, if you are doing significant secondary or primary research toward your Independent Capstone in a semester prior to registering for ANTH 3993, you may ask your faculty mentor to supervise an independent study, directed reading, or directed research class (as appropriate) with the number of credits appropriate to the work you are doing.

However, even if your project can be completed in a two-semester period, you should already have identified a faculty member who is willing to supervise your research prior to the start of the semester in which you are registered for ANTH 3993 so that you can get started on your research immediately. 

Ethics Review

Additionally, please note that if your research involves human or animal subjects (that is, living people or animals), you will need to submit your proposed research for review to the appropriate university ethics review committee. Almost always, student research is considered “exempt” from full review, but that decision must be made by the relevant committee.  As such, regardless of when you undertake the research, you must go through this process prior to active research involving human or animal subjects. It is usually a relatively quick step, but an essential one.

Reasons for registering for the Independent Capstone Option

There are several—and not mutually exclusive —reasons that a student may opt for the Independent Capstone Option.

• First, this option is ideal for students who simply have a question that intrigues them and that they seek to answer through research. 
• Second, students who have already decided to pursue anthropological research as a career will be well served by the Independent Capstone option in the subfield they intend to pursue. 
• Third, a student who plans to pursue graduate study in any field will benefit from this option by demonstrating their ability to conduct independent research to a graduate admissions committee when they submit their graduate school applications.

ANTH 3993 will be graded by your faculty mentor.

SEMESTER II

The following semester, you will register for the Independent Capstone Project II (ANTH 4013 or 4013H) . This is a 3-credit class designed to provide support to students carrying out and writing research, in a structured writing workshop format. While attending this class, students may continue to carry out late-stage research or analysis and will also meet regularly with their faculty mentor. However, since the class is designed to take all registered students through the process of writing, it is strongly recommended that you complete the majority of your primary research prior to the start of this semester. 

The outcome of the class will be a completed independent capstone project which will be jointly graded by the student’s faculty adviser (whose assessment will count for 75% of the grade) and the instructor of ANTH 4013/H (whose assessment will count for 25% of the grade).  

In addition, you will be expected to make a short oral presentation on your research findings to the department community at the end of the semester.

To register for the Independent Capstone I & II Option:

To register for either course in this two-semester sequence, contact the Departmental Administrator Taryn Verley ( [email protected] ) for permission numbers. You must have completed ANTH 3993 prior to registering for ANTH 4013.

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Office of Undergraduate Education

University Honors Program

• Honors Requirements
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Northern Minnesota Mining (Summer 2024)

Northern Minnesota - home to a diverse community and environment that includes Indigenous Nations, a thriving tourist industry, the Boundary Waters Canoe Area, and a wealth of critical metals needed to shift to more sustainable energy sources - is the focus of this NEXUS Experience. Currently, there is intense debate around the establishment of mines in northern Minnesota that can provide metals necessary for the manufacturing of technology, specifically the metals needed to sustain green energy initiatives. The goal of this experience is to learn about the balance among our needs for cleaner energy, the mineral resources needed to shift to cleaner energy initiatives and the impacts of mining on the environment and cultures of the region.

We will be based for five days in mid-August (15 - 19) at the Hubachek Wilderness Research Center, a facility owned and operated by the UMN College of Food, Agricultural and Natural Resources Science. During our time up north we will explore the local geology and mineral resources, tour old and current iron mines, and learn about the diverse communities and cultures of the region. No background in Earth sciences or mining and mineral  resources is required.

Application opens 4/15

• Summer Research Opportunities
• Global Seminars and LAC Seminars
• Honors Research in London - Summer 2024