Secondary Mathematics Prerequisites

UChicago UTEP only accepts candidates for the Secondary Mathematics certification pathway who plan to teach in a Chicago Public Schools middle school or high school. Ideal candidates have or are working toward an undergraduate major or minor comparable to the collegiate mathematics program at the University of Chicago. Applicants should have at least a B average in their majors; grades for individual classes within the major should not be lower than a B-.

Secondary Mathematics applicants are expected to have completed two quarters or one semester of college-level Analysis and Abstract Algebra and be proficient in writing and understanding proofs applicable to each. Prospective applicants may want to consult Steven R. Lay's Analysis with an Introduction to Proof as a form of both self-assessment and preparation for the program.

  • Analysis: Metric spaces; compact sets; geometry of Euclidean space; limits and continuous mappings; partial differentiation; vector-valued functions; extrema; inverse and implicit function theorems; multiple integrals; line and surface integrals; theorems of Green Gauss and Stokes
  • Abstract Algebra: Groups, subgroups and permutation groups; rings and ideals; fields; vector spaces, linear transformations and matrices, and modules; canonical forms of matrices, quadratic forms and multilinear algebra 

These courses are described in the University of Chicago’s College Catalog. Secondary Mathematics candidates who have not taken college-level courses in these areas may be asked to enroll as full-time students and take Analysis and/or Abstract Algebra, in addition to one or more of the following:

  • Introduction to Analysis and Linear Algebra: Reading and writing proofs; fundamentals of theoretical mathematics; construction of real numbers; completeness and the least upper bound property; topology of the real line; structure of finite-dimensional vector spaces over the real and complex numbers
  • Geometry: Advanced topics in geometry, including Euclidean geometry, spherical and hyberbolic geometry; rigorous development from axiomatic systems, including the approach of Hilbert; lattice point geometry, projective geomtery and symmetry
  • Number Theory: Basic properties of the integers following from the division algorithm, primes and their distribution and congruences; existence of primitive roots; arithmetic functions; quadratic reciprocity; transcendental numbers

The University of Chicago does not issue student visa documents for this MAT program.