# Mathematics Minor Requirements

## 2020 - 2021 Catalog

## Mathematics minor

A **minor in mathematics** requires completion of 21 credits. A student may not complete both a major and a minor in mathematics. In meeting the requirements of this discipline-based minor, a student may not use more than nine credits used to meet the requirements of another major or minor.

- MATH 102, 201, 221, 222
- Two courses chosen from the following: MATH 311, 321, 343, 391, 392, and 393
- One additional course at the 300 level in mathematics

- Required courses:
- MATH 102 - Calculus II
FDR FM Credits 3 Prerequisite The equivalent of MATH 101 with C grade or better. Note: Students wanting to take this course should add to the waiting list when open; additional sections may be added Faculty Staff A continuation of MATH 101, including techniques and applications of integration, transcendental functions, and infinite series.

- MATH 201 - Bridges to Advanced Mathematics
FDR SC Credits 3 Prerequisite 6 credits of MATH courses or MATH 221 or 222 Faculty Staff The course explores various important mathematical constructions and ideas, with a particular emphasis on mathematical inquiry and reasoning. Topics include: sets, functions, equivalence relations, modular arithmetic, and basic properties of the integers, real numbers, and complex numbers.

- MATH 221 - Multivariable Calculus
FDR SC Credits 3 Prerequisite The equivalent of MATH 102 with a C grade or better or MATH 201 or 222 Motion in three dimensions, parametric curves, differential calculus of multivariable functions, multiple integrals, line integrals, and Green's Theorem.

- MATH 222 - Linear Algebra
FDR SC Credits 3 Prerequisite The equivalent of MATH 102 with a C grade or better or MATH 201 or 221 Linear algebra is the backbone of much of mathematics. Students in this course learn to identify and explain the basic principles, terminology, and theories used in linear algebra, and apply quantitative and/or qualitative reasoning skills to solve problems posed in linear algebra, primarily through applications of to both mathematics and the sciences, and also by writing proofs In mathematics.

- Two courses chosen from the following:
- MATH 311 - Real Analysis
Credits 3 Prerequisite MATH 201 (or 301) and 221 Faculty Staff A systematic study of concepts basic to calculus, such as topology of the real numbers, limits, differentiation, integration, sequences and series. Additional topics vary by instructor.

- MATH 321 - Abstract Algebra
Credits 3 Prerequisite MATH 201 (or 301) and 222 Faculty Staff An introduction to basic algebraic structures common throughout mathematics. These include rings, fields, groups, homomorphisms and quotient structures. Additional topics vary by instructor.

- MATH 343 - Geometry
Credits 3 Prerequisite MATH 201 (or 301) , 221, and 222 Faculty Staff This course is an introduction to geometric techniques through study of Euclidean and non-Euclidean geometries and their transformations. Additional topics vary by instructor.

- MATH 391 - Topics in Analysis
Credits 3 Prerequisite MATH 311 Topics vary but can include complex analysis, topology, differential equations, differential topology, numerical analysis, functional analysis, measure theory, fractal geometry, Lebesgue integration and Fourier analysis, harmonic analysis, and analytic number theory. May be repeated for degree credit if the topic is different.

- MATH 392 - Topics in Abstract Algebra
Credits 3 Prerequisite MATH 321 Topics vary but can include field and Galois theory, geometric and combinatorial group theory, representation theory, number theory, algebraic number theory, commutative algebra, algebraic geometry, arithmetic geometry, advanced linear algebra, algebraic coding theory and cryptography, algebraic topology, homological algebra, and graph theory, May be repeated for degree credit if the topic is different.

**Winter 2021, MATH 392A-01: Topics in Abstract Algebra: Algebraic Number Theory****(3).***Prerequisite: MATH 321.*Number theory studies questions about the integers (among other things). As an example, the equation x^2 + y^2 = z^2 defines a cone in three-dimensional space. A number theorist might ask for the integer triples (x,y,z) that satisfy this equation. These are also called Pythagorean triples since (ignoring signs) they arise as the side lengths of right-angled triangles. You may be aware that (3,4,5) and (5,12,13) are such triples. Are there others? Can they be described in a systematic fashion? What happens if we change the equation? In this course, we'll see how these sorts of questions can be addressed. Ideas and tools from algebra such as modular arithmetic and the notion of unique factorization in various systems will play central roles.*Bush.* - MATH 393 - Topics in Geometry and Topology
Credits 3 Prerequisite MATH 342 or 343 Topics vary but can include knot theory, topology and geometry of surfaces, differential geometry, Riemann surfaces, 3-manifolds, tilings, geometric probability, geometry of spacetime, finite geometry, computational geometry, differential topology, and projective geometry. May be repeated for degree credit if the topic is different.

**Winter 2021, MATH 393A-01: Topics in Geometry and Topology: Experimenting with Geometry (3).***Prerequisite: MATH 342 or 343.*This course will be run in an experimental format modeled on the notion of a "Geometry Lab." Students will study unsolved problems in geometry, learning whatever background material is relevant for understanding and approaching the selected problems. Topics are likely to include algebraic geometry, hyperbolic geometry, and projective geometry.*Abrams.* - One additional course at the 300 level in mathematics