Are you finishing your undergraduate program or preparing to apply to a graduate program and need to boost your math credits? The University of Illinois’ Netmath Program has increased its upper-level Grad School Prep and Applied Mathematics Prep courses in an effort to better serve students.

NetMath is the online self-paced distance learning program of the Department of Mathematics at Illinois, and all courses have been recorded by distinguished Mathematics faculty. Many students take the courses to complete their degree programs and prepare for their graduate school applications.

Take a look at the Graduate Prep Courses (for highly Mathematical/Proof-oriented programs):

Math 416: Abstract Linear Algebra (3 credit hours) is a rigorous, abstract treatment of linear algebra. Topics 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. 

Math 417: Abstract Algebra (3 hours) 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.

Math 447: Real Variables (3 hours) is a 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.

Math 448: Complex Variables (3 hours) 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.

Take a look at the Applied Math Prep Courses (for applied Mathematical graduate programs):

Math 415: Applied Linear (3 hours) is an 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.

Math 423: Differential Geometry (3 hours) 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.

Math 442: Intro to Partial Differential Equations (3 hours) covers the 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.

Math 444: Elementary Real Analysis (3 hours) 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 include the real number system, limits, continuity, derivatives, the Darboux integral, the Riemann integral, and sequences of functions.

Math 446: Applied Complex Variables (3 hours) is 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. Students desiring a systematic development of the foundations of the subject should take MATH 448.

Math 461: Probability Theory (3 hours) is an introduction to mathematical probability; includes the calculus of probability, combinatorial analysis, random variables, expectation, distribution functions, moment-generating functions, and central limit theorem.

Math 481: Vector and Tensor Analysis (3 hours) is an 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.

Courses begin on the date your registration is processed, and you have 16 weeks from the date of registration to complete the course. Upon registration, the NetMath office will notify you of your official course start and end date. The 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.

For more information on NetMath and these courses, go to: https://netmath.illinois.edu/academics/netmath-courses-college-students.