Subject |
Number |
Title |
Hours |
Catalog Description |
General Education Category |

MATH | 070 | Elementary Mathematics | 3 hours. | Rational operations and arithmetic, fundamental operations of algebra, linear equations and polynomials, graphing. Satisfactory/Unsatisfactory grading only. Not open to students with credit in MATH 090, MATH 092 or a mathematics course at or above the 100 level. No graduation credit. Prerequisite(s): Eligibility determined by performance on the department placement test. | |

MATH | 075 | Beginning Algebra | 2 hours. | Linear equations and inequalities, functions, linear functions, slope, exponents, polynomials, quadratic equations, rational expressions, rational equations, and applications. Satisfactory/Unsatisfactory grading only. Not open to students with credit in Math 070, 090, or a mathematics course at or above the 100-level. No graduation credit. Prerequisite(s): Appropriate score on the department placement test. | |

MATH | 090 | Intermediate Algebra | 5 hours. | Linear equations, rational expressions, quadratic equations, graphing, exponentials and logarithms, systems of linear equations. Satisfactory/Unsatisfactory grading only. Not open to students with credit in MATH 092 or a mathematics course at or above the 100 level. No graduation credit. Prerequisite(s): Math 070 or MATH 075, or appropriate performance on the UIC mathematics test. | |

MATH | 118 | Mathematical Reasoning | 5 hours. | Elementary topics from algebra applied to descriptive statistics of data, scatter plots, correlation, linear regression, probability, random samples, sampling distributions, experimental designs. Graphing calculator used. No credit given if the student has credit in MATH 150 or 160 or 165 or 180, or the equivalent. No credit given if the student has credit in MATH 121 with a grade of C or better. No graduation credit for architecture, business administration, or engineering students. The only mathematics department course for which MATH 118 serves as a prerequisite is MATH 123. It may serve as a preprequisite for statistics courses in the social sciences. It does not replace MATH 090 as a prerequisite for any other mathematics department course. Prerequisite(s): MATH 070, or MATH 075, or appropriate performance on the UIC mathematics placement test. | |

MATH | 121 | Precalculus Mathematics | 5 hours. | Logarithms, radicals, graphing of rational functions, complex numbers, trigonometry, DeMoivre's formula, theory of equations, sequences, systems of linear equations. No credit for students who have credit in MATH 165, MATH 180, or MATH 205. No graduation credit for architecture, business administration, or engineering students. Prerequisite(s): MATH 090 or MATH 092 or appropriate performance on the UIC mathematics placement test. | |

MATH | 122 | Emerging Scholars Workshop for Precalculus Mathematics | 1 hours. | Intensive math workshop for students enrolled in MATH 121. Students work together in groups to solve challenging problems. Satisfactory/Unsatisfactory grading only. Prerequisite(s): Admission to the Emerging Scholars Program. Must enroll concurrently in MATH 121. | |

MATH | 123 | Quantitative Reasoning | 5 hours. | Choice of models for real-world problems, using elementary functions, linear equations, and graphs. Statistical data analysis, confidence intervals, estimation, testing. Graphing calculator and PC applications. No credit given if the student has credit in MATH 150 or 160 or 165 or 180, or the equivalent. No credit given if the student has credit in MATH 121 with a grade of C or better. No graduation credit for architecture, business administration, or engineering students. Prerequisite(s): Grade of C or better in MATH 118. | |

MATH | 125 | Elementary Linear Algebra | 5 hours. | Introduction to systems of linear equations, matrices and vector spaces, with emphasis on business applications. Prerequisite(s): Math 090 or grade of C or better in Math 121 or appropriate performance on the UIC mathematics placement test. | |

MATH | 140 | Arithmetic and Algebraic Structures | 4 hours. | Introduction to conceptual foundations of mathematics. Topics include measurement, numeration, number theory, set theory, equations in one variable. Use of full purpose calculator throughout. Prerequisite(s): MATH 090 or MATH 092 or appropriate performance on the UIC mathematics placement test. | |

MATH | 141 | Algebraic and Geometric Structures | 4 hours. | Area, perimeter, volume, surface area of plane and solid figures; integers, real and rational numbers; trigonometry and extended solution of general polygons; probability. Full purpose calculators used. Designed for students in the B.A. in Elementary Education program. Prerequisite(s): Grade of C or better in MATH 140. | |

MATH | 145 | Effective Thinking from Mathematical Ideas | 4 hours. | Investigates diverse mathematical concepts and highlights effective methods of reasoning relevant to real life. Topics include reasoning about numbers, infinity, the fourth dimension, topological space, chaos and fractals, and analyzing chance. Prerequisite(s): MATH 090 or MATH 092 or appropriate performance on the UIC mathematics placement test or consent of the instructor. | |

MATH | 160 | Finite Mathematics for Business | 5 hours. | Introduction to probability, statistics, and matrices, with emphasis on business applications. Math 090 or grade of C or better in Math 121 or appropriate performance on the UIC mathematics placement test. | Natural World - No Lab course. |

MATH | 165 | Calculus for Business | 5 hours. | Introduction to differential and integral calculus of algebraic, exponential and logarithmic functions and techniques of partial derivatives and optimization. Emphasis on business applications. Credit is not given for MATH 165 if the student has credit for MATH 180. Prerequisite(s): Math 090 or grade of C or better in Math 121 or appropriate performance on the UIC mathematics placement test. | Natural World - No Lab course. |

MATH | 179 | Emerging Scholars Workshop for Calculus I | 1 hours. | Intensive math workshop for students enrolled in MATH 180. Students work together in groups to solve challenging problems. Satisfactory/Unsatisfactory grading only. Prerequisite(s): Admission to the Emerging Scholars Program. Must enroll concurrently in MATH 180. | |

MATH | 180 | Calculus I | 5 hours. | Differentiation, curve sketching, maximum-minimum problems, related rates, mean-value theorem, antiderivative, Riemann integral, logarithm, and exponential functions. Credit is not given for MATH 180 if the student has credit for MATH 165. Prerequisite(s): Grade of C or better in Math 121 or appropriate performance on the department placement test. | Natural World - No Lab course. |

MATH | 181 | Calculus II | 5 hours. | Techniques of integration, arc length, solids of revolution, applications, polar coordinates, parametric equations, infinite sequences and series, power series. Prerequisite(s): Grade of C or better in MATH 180. | Natural World - No Lab course. |

MATH | 182 | Emerging Scholars Workshop for Calculus II | 1 hours. | Intensive math workshop for students enrolled in MATH 181. Students work together in groups to solve challenging problems. Satisfactory/Unsatisfactory grading only. Prerequisite(s): Admission to the Emerging Scholars Program. Must enroll concurrently in MATH 181. | |

MATH | 194 | Special Topics in Mathematics | 1 TO 4 hours. | Course content is announced prior to each term in which it is given. May be repeated. Prerequisite(s): Approval of the department. | |

MATH | 210 | Calculus III | 3 hours. | Vectors in the plane and space, vector valued functions, functions of several variables, partial differentiation, maximum-minimum problems, double and triple integrals, applications, Green's theorem. Prerequisite(s): Grade of C or better in MATH 181. | Natural World - No Lab course. |

MATH | 211 | Emerging Scholars Workshop for Calculus III | 1 hours. | Intensive math workshop for students enrolled in MATH 210. Students work together in groups to solve challenging problems. Satisfactory/Unsatisfactory grading only. Prerequisite(s): Admission to the Emerging Scholars Program. Must enroll concurrently in MATH 210. | |

MATH | 215 | Introduction to Advanced Mathematics | 3 hours. | Introduction to methods of proofs used in different fields in mathematics. Prerequisite(s): Grade of C or better in MATH 181 and approval of the department. | |

MATH | 220 | Introduction to Differential Equations | 3 hours. | Techniques and applications of differential equations. First order equations: separable and linear. Linear second order equations, Laplace transforms, and series solutions. Graphical and numerical methods. Fourier series and partial differential equations. Prerequisite(s): Grade of C or better in MATH 210. | |

MATH | 294 | Special Topics in Mathematics | 1 TO 4 hours. | Course content is announced prior to each term in which it is given. May be repeated. Prerequisite(s): Approval of the department. | |

MATH | 300 | Writing for Mathematics | 1 hours. | Fulfills Writing-in-the-Discipline requirement. Prerequisite(s): ENGL 161 or the equivalent, and a grade of C or better in MATH 210. Students must have declared a major in the Mathematics, Statistics, and Computer Science Department. | |

MATH | 310 | Applied Linear Algebra | 3 hours. | Matrices, Gaussian elimination, vector spaces, LU-decomposition, orthogonality, Gram-Schmidt process, determinants, inner products, eigenvalue problems, applications to differential equations and Markov processes. Credit is not given for MATH 310 if the student has credit for MATH 320. Prerequisite(s): Grade of C or better in MATH 210. | |

MATH | 313 | Analysis I | 3 hours. | The real number system, limits, continuous functions, differentiability, the Riemann integral. Prerequisite(s): Grade of C or better in MATH 215 or consent of the instructor. | |

MATH | 320 | Linear Algebra I | 3 hours. | Linear equations, Gaussian elimination, matrices, vector spaces, linear transformations, determinants, eigenvalues and eigenvectors. Credit is not given for MATH 320 if the student has credit for MATH 310. Prerequisite(s): Concurrent registration in MATH 215. | |

MATH | 330 | Abstract Algebra I | 3 hours. | Sets, properties of integers, groups, rings, fields. Prerequisite(s): Grade of C or better in MATH 215. | |

MATH | 394 | Special Topics in Mathematics | 2 TO 4 hours. | Course content is announced prior to each term in which it is given. May be repeated. Students may register in more than one section per term. Prerequisite(s): Approval of the department. | |

MATH | 410 | Advanced Calculus I | 3 OR 4 hours. | Functions of several variables, differentials, theorems of partial differentiation. Calculus of vector fields, line and surface integrals, conservative fields, Stokes's and divergence theorems. Cartesian tensors. 3 undergraduate hours. 4 graduate hours. Prerequisite(s): Grade of C or better in MATH 210. | |

MATH | 411 | Advanced Calculus II | 3 OR 4 hours. | Implicit and inverse function theorems, transformations, Jacobians. Point-set theory. Sequences, infinite series, convergence tests, uniform convergence. Improper integrals, gamma and beta functions, Laplace transform. 3 undergraduate hours. 4 graduate hours. Prerequisite(s): Grade of C or better in MATH 410. | |

MATH | 414 | Analysis II | 3 OR 4 hours. | Sequences and series of functions. Uniform convergence. Taylor's theorem. Topology of metric spaces, with emphasis on the real numbers. 3 undergraduate hours. 4 graduate hours. Prerequisite(s): Grade of C or better in MATH 313. | |

MATH | 417 | Complex Analysis with Applications | 3 OR 4 hours. | Complex numbers, analytic functions, complex integration, Taylor and Laurent series, residue calculus, branch cuts, conformal mapping, argument principle, Rouche's theorem, Poisson integral formula, analytic continuation. 3 undergraduate hours. 4 graduate hours. Prerequisite(s): Grade C or better in MATH 210. | |

MATH | 419 | Models in Applied Mathematics | 3 OR 4 hours. | Introduction to mathematical modeling; scaling, graphical methods, optimization, computer simulation, stability, differential equation models, elementary numerical methods, applications in biology, chemistry, engineering and physics. 3 undergraduate hours. 4 graduate hours. Prerequisite(s): Grade of C or better in MATH 220 and grade of C or better in MCS 260. | |

MATH | 425 | Linear Algebra II | 3 OR 4 hours. | Canonical forms of a linear transformation, inner product spaces, spectral theorem, principal axis theorem, quadratic forms, special topics such as linear programming. 3 undergraduate hours. 4 graduate hours. Prerequisite(s): Grade of C or better in MATH 320. | |

MATH | 430 | Formal Logic I | 3 OR 4 hours. | First order logic, syntax and semantics, completeness-incompleteness. 3 undergraduate hours. 4 graduate hours. Credit is not given for MATH 430 if the student has credit for PHIL 416. Prerequisite(s): Grade of C or better in CS 202 or grade of C or better in MCS 261 or grade of C or better in MATH 215. | |

MATH | 431 | Abstract Algebra II | 3 OR 4 hours. | Further topics in abstract algebra: Sylow Theorems, Galois Theory, finitely generated modules over a principal ideal domain. 3 undergraduate hours. 4 graduate hours. Prerequisite(s): Grade of C or better in MATH 320 and grade of C or better in MATH 330. | |

MATH | 435 | Foundations of Number Theory | 3 OR 4 hours. | Primes, divisibility, congruences, Chinese remainder theorem, primitive roots, quadratic residues, quadratic reciprocity, and Jacobi symbols. The Euclidean algorithm and strategies of computer programming. 3 undergraduate hours. 4 graduate hours. Prerequisite(s): Grade of C or better in MATH 215. | |

MATH | 436 | Number Theory for Applications | 3 OR 4 hours. | Primality testing methods of Lehmer, Rumely, Cohen-Lenstra, Atkin. Factorization methods of Gauss, Pollard, Shanks, Lenstra, and quadratic sieve. Computer algorithms involving libraries and nested subroutines. 3 undergraduate hours. 4 graduate hours. Prerequisite(s): Grade of C or better in MATH 435. | |

MATH | 442 | Differential Geometry of Curves and Surfaces | 3 OR 4 hours. | Frenet formulas, isoperimetric inequality, local theory of surfaces, Gaussian and mean curvature, geodesics, parallelism, and the Guass-Bonnet theorem. 3 undergraduate hours. 4 graduate hours. Prerequisite(s): Grade of C or better in MATH 320. | |

MATH | 445 | Introduction to Topology I | 3 OR 4 hours. | Elements of metric spaces and topological spaces including product and quotient spaces, compactness, connectedness, and completeness. Examples from Euclidean space and function spaces. 3 undergraduate hours. 4 graduate hours. Prerequisite(s): Grade of C or better in MATH 313. | |

MATH | 446 | Introduction to Topology II | 3 OR 4 hours. | Topics in topology chosen from the following: advanced point set topology, piecewise linear topology, fundamental group and knots, differential topology, applications to physics and biology. 3 undergraduate hours. 4 graduate hours. Prerequisite(s): Grade of C or better in MATH 445. | |

MATH | 480 | Applied Differential Equations | 3 OR 4 hours. | Linear first-order systems. Numerical methods. Nonlinear differential equations and stability. Introduction to partial differential equations. Sturm-Liouville theory. Boundary value problems and Green's functions. 3 undergraduate hours. 4 graduate hours. Prerequisite(s): Grade of C or better in MATH 220. | |

MATH | 481 | Applied Partial Differential Equations | 3 OR 4 hours. | Initial value and boundary value problems for second order linear equations. Eiqenfunction expansions and Sturm-Liouville theory. Green's functions. Fourier transform. Characteristics. Laplace transform. 3 undergraduate hours. 4 graduate hours. Prerequisite(s): Grade of C or better in MATH 220. | |

MATH | 494 | Special Topics in Mathematics | 3 OR 4 hours. | Course content is announced prior to each term in which it is given. 3 undergraduate hours. 4 graduate hours. May be repeated. Students may register in more than one section per term. Prerequisite(s): Approval of the department. | |

MATH | 496 | Independent Study | 1 TO 4 hours. | Reading course supervised by a faculty member. May be repeated. Students may register in more than one section per term. Prerequisite(s): Approval of the instructor and the department. |