# Mathematics Minor Requirements

## 2021 - 2022 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, infinite series, and parametric curves.

- 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, 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.

**Fall 2021, MATH 391A-01: Topics in Analysis: Numerical Mathematics for Data Science (3).***Prerequisite: MATH 311.*This course is designed to introduce knowledge of numerical computation and analysis, in order to equip students with necessary numerical techniques to address practical questions arising from data science and other fields. We will discuss useful methods to construct mathematical models from given data and powerful algorithms to solve large scale systems of linear equations which are formulated during the creation of mathematical models. Students will also learn computational complexity, accuracy, stability, conditioning, and other mathematical concepts of numerical analysis which are fundamental in developing an efficient numerical algorithm. MATLAB will be the programming language used for this course.*Wang.* - 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 2022, Math 392A-01: Topics in Abstract Algebra: Rings, Fields, and Galois Theory (3).***Prerequisite: MATH 321.*Rings, ring homomorphisms, modules, module homomorphisms, Euclidean domains, PIDs, UFDs, field extensions, degree, algebraic numbers, automorphisms, irreducible polynomials, Galois groups, Galois correspondence.*Colbert.* - 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 2022, Math 393A-01: Topics in Geometry and Topology: Differential Topology (3).***Prerequisite: Math 342 or 343.*This course builds on material from multivariable calculus, linear algebra and geometry. We cover a range of topics: an introduction to manifolds with boundary, derivatives as linear transformations, tangent spaces, inverse and implicit function theorems, transversality, and intersections of manifolds. Then integration on manifolds, differential forms, and the generalized Stokes's Theorem.*Denne.***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