MATH 012 (112). College Algebra
Syllabus
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. Stu-
dents who need both algebra and trigonometry should enroll in MATH 016. Credit
is not given for both MATH 012 and MATH 016. Credit not applicable toward grad-
uation in certain curricula. Prerequisite: 1.5 units of high school algebra; 1 unit of
high school geometry.
MATH 016 (116). Algebra and Trigonometry
Syllabus for Mathematica based section
Syllabus for ALEKS based section
Unified treatment of algebra and trigonometry.
Prerequisite: 1 1/2 units of high school algebra; 1 unit of high school geometry. Credit not applicable toward graduation in certain colleges. 5 hours.
As an additional prerequisite, Math 016 requires instructor approval. Please contact Debra Woods, via netmathinfo@cm.math.uiuc.edu, proir to registration. This requirement applies only to Math 016.
MATH 115. Preparation for Calculus
Syllabus
Reviews trigonometric, rational, exponential, and logarithmic functions; provides a full
treatment of limits, definition of derivative, and an introduction to finding area under a curve. Intended
for students who need preparation for MATH 220 (calculus 1), either because they lack the content background
or because they are not prepared for the rigor of a university calculus course. Credit is not given for BOTH
MATH 115 and either MATH 014 or MATH 016. Students may not receive credit for MATH 115 if MATH 115 is taken
after receiving credit for MATH 220 or MATH 221.
Prerequisite: MATH 012 or equivalent.
MATH 220 (120). Calculus and Analytic Geometry, I
Syllabus
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.
Prerequisite: Mathematics 016; or Mathematics 012 and 014. Credit is not given for both Mathematics 220 and either 221 or 234. 5 hours.
Before enrolling in Math 220, be sure you are familiar with these types of functions.
MATH 231 (130). Calculus and Analytic
Geometry, II
Syllabus
Second course in calculus and analytic geometry: techniques of integration, conic sections, polar coordinates, and infinite series.
Prerequisite: Mathematics 220. Credit is not given for both Mathematics 230 and 231. 3 hours.
Before enrolling in Math 231, be sure you are familiar with these concepts from calculus 1.
MATH 234 (134). Calculus for Business, I
Syllabus
Introduction to the concept of functions and the basic ideas of calculus.
Prerequisite: Math 012. 4 hours.
MATH 290. Symbolic Computation Lab
Laboratory component to courses using a symbolic programming package.
Prerequisite: Consent of department; concurrent registration in a designated section of a mathematics course with symbolic computation component. May be taken only once for credit. 1 hour.
MATH 225. Introductory Matrix Theory
Syllabus
Systems of linear equations, matrices and inverses, determinants, and a glimpse at vector spaces, eigenvalues and eigenvectors.
Prerequisite: Mathematics 220 or equivalent. 2 hours. Credit is not given for both Mathematics 225 and 125. Also, students with earned credit in Mathematics 315 may not receive additional credit for Mathematics 225, when 225 is taken after 415.
MATH 241 Calculus III
Syllabus
Third course in calculus and analytic geometry including: vector analysis, Euclidean space, partial differentiation, multiple integrals, line and surface integrals, the integral theorems of vector calculus. Credit is not given for more than one of the following: Math 241 and Math 242, Math 243, Math 244, or Math 380.
This course satisfies the General Education Criteria for a
Quant Reasoning II course.
Credit: 4 hours. Prerequisite: MATH 230 or MATH 231.
MATH 380 (280). Advanced Calculus
Syllabus
Introductory study of vector calculus and functions of several variables; topics include directional derivatives; Jacobians; change of variables in multiple integrals; maxima and minima; line and surface integrals; theorems of Gauss, Green, and Stokes; in finite series; and uniform convergence.
Prerequisite: One of Mathematics 242, 245, 230, 231, or equivalent. (Counts
for advanced hours in Liberal Arts and Sciences). Credit is not given
for both MATH 380 and MATH 241. 3 hours.
MATH 285 (385). Differential Equations and Orthogonal Functions
Syllabus
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.
Prerequisite: Mathematics 241. Credit is not given for both Mathematics 285 and any of Math 284, Math 286, Math 441. (Counts for advanced hours in Liberal Arts and Sciences. ) 3 hours.
Before enrolling in Math 285, be sure you are familiar with these concepts.
MATH 286. Intro to Differential Equations Plus
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 the MATH 285 plus linear systems. Intended for engineering majors and other who require a working knowledge of differential equations.
Credit is not given for both MATH 286 and any of MATH 284, MATH 285, MATH 441.
Prerequisite: MATH 241. 4 hours.
MATH 292. Vector Calculus Supplement
Course in multivariable calculus. Topic include gradient divergence, and curl; line and surface integrals; and the theorems of Green, Stokes, and Gauss. Intended for transfer students who multivariable calculus course did not include the integral theorems of vector calculus. Credit is not given for both MATH 292 and MATH 241. 2hours.
Prerequisite: Consent of instructor.
MATH 415 (315). Linear Transformations and Matrices
Syllabus
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. 4 hours of credit requires
approval of the instructor and department with completion of additional
work of substance. Credit is not given for both MATH 415 and any of
MATH 125, MATH 225, or MATH 410.
Prerequisite: Mathematics 241, 243, or equivalent. 3 hours.
NetMath 415: Credit earned in this course cannot be applied toward an online graduate-level certificate or degree offered through the Engineering and
Computer Science Online program.
MATH 461 (361). Introduction to Probability Theory, I
Syllabus
Introduction to mathematical probability; includes the calculus of probability, combinatorial analysis, random variables, expectation, distribution functions, moment-generating functions, and central limit theorem.
Prerequisite: Mathematics 241, 243, or equivalent. 3 hours.
NetMath 461: Credit earned in this course cannot be applied toward an online graduate-level certificate or degree offered through the Engineering and
Computer Science Online program.
