# NetMath Courses for College Students

## Overview

College students have 16 weeks from the date of registration to complete a NetMath course. Upon registration, students will receive communication from the NetMath office regarding their official course start and end date. These courses are self-paced, and students who are able to work at a faster pace may complete their coursework prior to their assigned end course date. Some courses allow a paid course extension: please check the specific course page for information on extensions, syllabus, cost, number of credit hours, and necessary course materials.

## Math Topics

Algebra — Math 112: Rapid review of basic techniques of factoring, rational expressions, equations and inequalities; functions and graphs; exponential and logarithm functions; systems of equations; matrices and determinants; polynomials; and the binomial theorem.

Trigonometry — Math 114: Studies degrees and radians, the trigonometric functions, identities and equations, inverse functions, oblique triangles and applications.

Calculus Prep — Math 115: This course reviews trigonometric, rational, exponential, and logarithmic functions, and introduces finding the area under a curve. Intended for students who need preparation for MATH 220, either because they lack the content background or because they are not prepared for the rigor of a university calculus course.

Finite Math — Math 124: This course introduces and explores various areas in finite mathematics, including systems of linear equations, matrices, input-output analysis, maximizing or minimizing linear functions of two or more variables subject to linear inequality constraints, sophisticated counting, mathematical probability, and the mathematics of finance.

### Algebra — Math 112

### Trigonometry — Math 114

### Calculus Prep — Math 115

### Finite Math — Math 124

Calculus I — Math 220: A first course in Calculus and Analytic Geometry; basic techniques of differentiation and integration with applications including curve sketching; antidifferentation, the Riemann integral, fundamental theorem, exponential and circular functions.

Calculus II — Math 231: Second course in calculus and analytic geometry. Topics include techniques and applications of integration, infinite sequences, power series, parametric equations, and an introduction to differential equations.

Business Calculus — Math 234: This is a standard course in Calculus with an emphasis on applications to business. Topics include functions, limits, continuity, the derivative, differentiation of functions with applications, exponential and logarithmic models, integration, Riemann sums, and the Fundamental Theorem of Calculus.

Calculus III — Math 241: Third course in calculus and analytic geometry. Topics include vector analysis, Euclidean space, partial differentiation, multiple integrals, line and surface integrals, and the integral theorems of vector calculus.

Vector Calculus Supplement — Math 292: Course in multivariable calculus. Topics include gradient divergence and curl; line and surface integrals; and the theorems of Green, Stokes, and Gauss. Intended for transfer students whose multivariable calculus course did not include the integral theorems of vector calculus.

Intro Differential Equations — Math 285: Intended for engineering students and others who require a working knowledge of differential equations; included are techniques and applications of ordinary differential equations and an introduction to partial differential equations.

Intro to Differential Eq Plus — Math 286: Techniques and applications of ordinary differential equations, including Fourier series and boundary value problems, linear systems of differential equations, and an introduction to partial differential equations. Covers all of MATH 285 plus linear systems. Intended for engineering majors and others who require a working knowledge of differential equations.

Differential Equations — Math 441: MATH 441 is a basic course in ordinary differential equations. Topics include existence and uniqueness of solutions and the general theory of linear differential equations. Treatment is more rigorous than that given in MATH 285.

Intro Partial Diff Equations — Math 442: This course covers basic theory of partial differential equations, with particular emphasis on the wave, diffusion, Laplace and Schrodinger equations. Topics include classification of PDEs in terms of order, linearity and homogeneity, finding the solutions of the PDEs using methods such as geometric, operator, Fourier, separation of variables and spherical means.

Applied Linear Algebra — Math 415: Introductory course emphasizing techniques of linear algebra with applications to engineering; topics include matrix operations, determinants, linear equations, vector spaces, linear transformations, eigenvalues and eigenvectors, inner products and norms, orthogonality, equilibrium, and linear dynamical systems.

Abstract Linear Algebra — Math 416: Math 416 is a rigorous, abstract treatment of linear algebra. Topics to be covered include vector spaces, linear transformations, eigenvalues and eigenvectors, diagonalizability, and inner product spaces. The course concludes with a brief introduction to the theory of canonical forms for matrices and linear transformations.

Elementary Real Analysis — Math 444: This course is an introduction to ε - δ analysis on real numbers, which makes what the students have learned from calculus courses rigorous. This course is for students who do not plan to do graduate study in Mathematics (those students should take Math 447). Topics covered in Math 444 include the real number system, limits, continuity, derivatives, the Darboux integral, the Riemann integral, and sequences of functions.

Applied Complex Variables — Math 446: For students who desire a working knowledge of complex variables; covers the standard topics and gives an introduction to integration by residues, the argument principle, conformal maps, and potential fields.

Real Variables — Math 447: Careful development of elementary real analysis for those who intend to take graduate courses in Mathematics. Topics include completeness property of the real number system; basic topological properties of n-dimensional space; convergence of numerical sequences and series of functions; properties of continuous functions; and basic theorems concerning differentiation and Riemann integration.

Complex Variables — Math 448: This course is for students who desire a rigorous introduction to the theory of functions of a complex variable. Topics include Cauchy's theorem, the residue theorem, the maximum modulus theorem, Laurent series, the fundamental theorem of algebra, and the argument principle.

Vector and Tensor Analysis — Math 481: Introductory course in modern differential geometry focusing on examples and broadly aimed at students in mathematics, the sciences, and engineering. Emphasis on rigorously presented concepts, tools and ideas rather than on proofs. The topics covered include differentiable manifolds, tangent spaces and orientability; vector and tensor fields; differential forms; integration on manifolds and Generalized Stokes' Theorem; Riemannian metrics, Riemannian connections and geodesics. Applications to configuration and phase spaces, Maxwell equations and relativity theory will be discussed.

Differential Geometry — Math 423: This course covers applications of calculus to the study of the shape and curvature of curves and surfaces; introduction to vector fields, differential forms on Euclidean spaces, and the method of moving frames for low-dimensional differential geometry.

Vector and Tensor Analysis — Math 481: Introductory course in modern differential geometry focusing on examples, broadly aimed at students in mathematics, the sciences, and engineering. Emphasis on rigorously presented concepts, tools and ideas rather than on proofs. The topics covered include differentiable manifolds, tangent spaces and orientability; vector and tensor fields; differential forms; integration on manifolds and Generalized Stokes' Theorem; Riemannian metrics, Riemannian connections and geodesics. Applications to configuration and phase spaces, Maxwell equations and relativity theory will be discussed.

Abstract Linear Algebra — Math 416: Math 416 is a rigorous, abstract treatment of linear algebra. Topics to be covered include vector spaces, linear transformations, eigenvalues and eigenvectors, diagonalizability, and inner product spaces. The course concludes with a brief introduction to the theory of canonical forms for matrices and linear transformations.

Abstract Algebra — Math 417: Math 417 is an introduction to abstract algebra. The main objects of study are groups, which are abstract mathematical objects that reflect the most basic features of many other mathematical constructions. We will also study rings and fields and other abstract mathematical objects, which can be thought of as groups with additional structure.

Real Variables — Math 447: Careful development of elementary real analysis for those who intend to take graduate courses in Mathematics. Topics include completeness property of the real number system; basic topological properties of n-dimensional space; convergence of numerical sequences and series of functions; properties of continuous functions; and basic theorems concerning differentiation and Riemann integration.

Complex Variables — Math 448: This course is for students who desire a rigorous introduction to the theory of functions of a complex variable. Topics include Cauchy's theorem, the residue theorem, the maximum modulus theorem, Laurent series, the fundamental theorem of algebra, and the argument principle.

Applied Linear Algebra — Math 415: Introductory course emphasizing techniques of linear algebra with applications to engineering; topics include matrix operations, determinants, linear equations, vector spaces, linear transformations, eigenvalues and eigenvectors, inner products and norms, orthogonality, equilibrium, and linear dynamical systems.

Differential Geometry — Math 423: This course covers applications of calculus to the study of the shape and curvature of curves and surfaces; introduction to vector fields, differential forms on Euclidean spaces, and the method of moving frames for low-dimensional differential geometry.

Differential Equations of 1-variable (Math 285, 286 and Math 441)

Intro to Partial Differential Equations — Math 442: This course covers basic theory of partial differential equations, with particular emphasis on the wave, diffusion, Laplace and Schrodinger equations. Topics include classification of PDEs in terms of order, linearity and homogeneity, finding the solutions of the PDEs using methods such as geometric, operator, Fourier, separation of variables and spherical means.

Elementary Real Analysis — Math 444: This course is an introduction to ε - δ analysis on real numbers, which makes what the students have learned from calculus courses rigorous. This course is for students who do not plan to do graduate study in Mathematics (those students should take Math 447). Topics covered by Math 444 include the real number system, limits, continuity, derivatives, the Darboux integral, the Riemann integral, and sequences of functions.

Applied Complex Variables — Math 446: For students who desire a working knowledge of complex variables; covers the standard topics and gives an introduction to integration by residues, the argument principle, conformal maps, and potential fields.

Probability Theory — Math 461: Introduction to mathematical probability; includes the calculus of probability, combinatorial analysis, random variables, expectation, distribution functions, moment-generating functions, and central limit theorem.

Vector and Tensor Analysis — Math 481: Introductory course in modern differential geometry focusing on examples, broadly aimed at students in mathematics, the sciences, and engineering. Emphasis is on rigorously presented concepts, tools and ideas rather than on proofs. Topics covered include differentiable manifolds, tangent spaces and orientability; vector and tensor fields; differential forms; integration on manifolds and Generalized Stokes' Theorem; Riemannian metrics, Riemannian connections and geodesics. Applications to configuration and phase spaces, Maxwell equations and relativity theory will be discussed.

Statistical Analysis — Stat 200: Statistics provides the tools to sort through data to make objective decisions. Stat 200 provides an accelerated introduction to the basic tools for quantitively oriented students, with particular emphasis on understanding which tools are appropriate for which problems. We cover experimental design (including basics of causal inference from observations), basic probability (both frequentist and Bayes), descriptive statistics, inference from samples (including null hypothesis significance tests), analysis of variance, multiple regression, logistic regression, and non-parametric methods. We include both an easy-to-use data analysis program and exercises in the R programming language.

Vector Calculus Supplement — Math 292: Course in multivariable calculus. Topics include gradient divergence, and curl; line and surface integrals; and the theorems of Green, Stokes, and Gauss. Intended for transfer students whose multivariable calculus course did not include the integral theorems of vector calculus.

NetMath Certificate Capstone Course — Math 299: Math 299 is the final course towards qualifying for the NetMath certificate program.

This course involves writing a paper to demonstrate and apply the knowledge you have gained from taking NetMath courses. There are no quizzes or exams, and the course grade is based on the following:

- Proposal for capstone paper (30%)

- Capstone paper (60%)

- Communication with instructor (10%)

Intro to Abstract Algebra — Math 417: The main objects of study here are groups, which are abstract mathematical objects that reflect the most basic features of many other mathematical constructions. We will also study rings and fields and other abstract mathematical objects, which can be thought of as groups with additional structure.

Elementary Theory of Numbers — Math 453: This course is a basic introduction to the theory of numbers. Core topics include divisibility, primes and factorization, congruences, arithmetic functions, quadratic residues and quadratic reciprocity, primitive roots and orders. Additional topics covered include sums of squares, Diophantine equations, and continued fractions. This course satisfies the General Education Criteria for Quantitative Reasoning II.

Probability Theory — Math 461: Introduction to mathematical probability; includes the calculus of probability, combinatorial analysis, random variables, expectation, distribution functions, moment-generating functions, and central limit theorem.

## To Register

Before starting your registration, please review NetMath Registration Process.

## Future Registration

Your NetMath course will begin immediately when your registration application is processed. Once you submit a registration application and confirm your intent to enroll, there is no mechanism to pause your course or start at a later date. If you are planning to register for a NetMath course in the future and would like to receive course reminders from the NetMath office, please click here.

## Note the following before registering:

**Please Note: Students currently registered in a University of Illinois Graduate Degree program will be restricted from registering in 16-week Academic Year-term NetMath courses. Matriculating UIUC Grad students will be allowed to register in Summer Session II NetMath courses. **

- You may enroll in one course at a time.
- Depending on how much information is required, your registration will take 5-10 business days to be processed.
- Once you confirm your intent to enroll you will be registered in that course within the next few days barring any account holds or advising holds.
- Click
**here**to register. The direct link is https://apps.citl.illinois.edu/non-degree-registration/Account/Login.- Note: Our registration site is run by the campus CITL (Center for Innovation in Teaching & Learning) office. If you are a new student, you will need to create an account to login.

## NetMath Course Extensions

Extensions are available for some courses (not intended for high school students). Click here to learn more.