College Math Courses and Classes Overview

Essential Information

In general, math courses are divided by entry-level, upper and graduate levels. Math courses at colleges and universities are intended to satisfy basic general education requirements for undergraduates and also provide the math major with advanced practice and knowledge in all areas of mathematics. Math majors can choose a concentration area, such as math education, applied math and general math. There are also minors in math.

Here is an overview of math concepts covered at the undergraduate and graduate level for math- and non-math majors:

  • Calculus
  • Statistical theories and methods
  • Analysis in math
  • Differential equations
  • Introductory and advanced algebra
  • Mathematical logic
  • Curvature in geometry

List of Courses

First-Year Calculus

This course is required of math majors. Topics include inverse trigonometric and logarithmic functions, applications involving work and pressure, techniques of integrations, and Taylor's formula. Students also explore power series, infinite series, numerical methods, polar coordinates and differential equations. Courses often use examples and problems encountered in business, social sciences and economics.

Linear Algebra

Students in this course, required for math majors, are introduced to the basic concepts of matrix algebra. Areas covered include the rank and characteristic roots of a matrix, along with unitary, linear and orthogonal transformations. Other topics include quadratic, Hermitian and bilinear forms. Coursework is presented using problems in the physical and biological sciences and economics.

Introduction to Abstract Algebra

The concepts and principles of modern abstract algebra include rings, groups and fields, the theory of equations, number theory and geometry. Also addressed are Abelian and non-Abelian groups, finite fields and integral domains. This course is for students wishing to pursue a degree in mathematics.

Probability and Statistics

A course for math- and non-math majors alike, this class is useful in many fields, and it usually satisfies a general education requirement. Coursework covers basic probability theory, random variables, expectation, correlation and limit theorems. Statistics topics include point estimation, central limit theorem, multivariate normal distributions, linear models and tests of hypotheses.

Differential Geometry

This advanced course for math and physics majors addresses the study of surfaces and curves in Euclidean space using concepts taught in linear algebra and integral calculus. Core topics include Frenet-Serret frames, Gaussian curvature, geodesics, holonomy, complex variables and the Gauss-Bonnet theorem.

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