Undergraduates.

Mathematics Requirements

Basic Courses Required of All EE and ECE Majors

All EE and ECE majors must successfully complete, or receive Advanced Placement Credit, for each of the following basic mathematics disciplines:

• MATH 31 or MATH 31L: Introductory Calculus I. Functions, limits, continuity, trigonometric functions, techniques and applications of differentiation, indefinite and definite integrals, the fundamental theorem of calculus.
• MATH 32 or MATH 32L: Introductory Calculus II. Transcendental functions, techniques and applications of integration, indeterminate forms, improper integrals, infinite series.
• MATH 103 or MATH 103L: Intermediate Calculus. Partial differentiation, multiple integrals, and topics in differential and integral vector calculus, including Green's theorem, the divergence theorem, and Stoke's theorem.
• STA 113 or MATH 135 or ECE 255: Probability/Statistics. If only one course is taken in probability and statistics, then STA 113, Probability and Statistics in Engineering, or ECE 255, Probability for Electrical and Computer Engineers, is recommended. STA 113 provides an introduction to probability, independence, conditional independence, Bayes' theorem; discrete and continuous, univariate and multivariate distributions; linear and nonlinear transformations of random variables; classical and Bayesian inference, decision theory, and comparison of hypotheses; and experimental design, statistical quality control, and other applications in engineering. ECE 255 is an upper-level course introducing basic concepts and techniques for the stochastic modeling of systems, including elements of probability, statistics, queuing theory and estimation. Students who wish to have a more in-depth treatment of probability theory per se may take MATH 135. (STA 113 and MATH 135 may be taken before or after the two required advanced courses described below; ECE 255 requires at least one of those as a prerequisite. Most students take the advanced math courses directly after completing MATH 103.)

Students who receive Advanced Placement credit for MATH 31 and who choose to enter MATH 32 directly will be considered to have met the completion requirement for MATH 31. Similarly, students who have received AP credit for both MATH 31 and MATH 32 and who choose to enter MATH 103 directly will be considered to have met the completion requirement for both MATH 31 and MATH 32. Engineering students should consider placing out of both MATH 31 and MATH 32 only if they have a score of 5 on the advanced section of the Math AP test and feel very confident with integral calculus.

Students who do not have AP (or transfer) credit for MATH 31 and who choose to enter MATH 32 or MATH 41 directly (on the basis of strong prior preparation) will be considered to have met graduation requirements provided they complete each of the remaining five required courses with grades of A or B. However, if they receive a grade of C+ or below in any one or more of those courses, they must take an additional MATH course and successfully retake any failed course. Other similar options are possible for students able to enter directly into still-higher-level MATH courses; programs should be discussed on a case-by-case basis with Dr. Ybarra or Dean Simmons.

Advanced Courses Required for All EE and ECE Majors

In addition to the above set of four required basic mathematics courses, all EE and ECE majors must take the following two advanced math courses designed specifically for engineering and science students:

• MATH 107: Linear Algebra and Differential Equations. Systems of linear equations, matrix operations, vector spaces, linear transformations, orthogonality, determinants, eigenvalues and eigenvectors, diagonalization, linear differential equations and systems with constant coefficients and applications, computer simulations. (Not open to students who have had MATH 104 or 111.)
• MATH 108: Ordinary and Partial Differential Equations. First and second order ordinary differential equations with applications, Laplace transforms, series solutions and qualitative behavior, Fourier series, partial differential equations, boundary value problems, Sturm-Liouville theory. (Not open to students who have had MATH 111 or 131.)

These two courses replace the former requirement (grandfathered for students who have already taken those courses and currently still recommended for students pursuing EE-MATH or ECE-MATH dual majors) that EE and ECE majors take either the two courses

• MATH 104: Linear Algebra and Applications. Systems of linear equations and elementary row operations, Euclidean n-space and subspaces, linear transformations and matrix representations, Gram-Schmidt orthogonalization process, determinants, eigenvectors and eigenvalues; applications.
• MATH 131: Elementary Differential Equations. Solution of differential equations of elementary types; formulation and integration of equations arising in applications. (Not open to students who have had MATH 111.)

or the two courses

• MATH 111: Applied Mathematical Analysis I. First and second order differential equations with applications; matrices, eigenvalues, and eigenvectors; linear systems of differential equations; Fourier series and applications to partial differential equations. (Not open to students who have had MATH 131.)
• MATH 114: Applied Mathematical Analysis II. Boundary value problems, complex variables, Cauchy's theorem, residues, Fourier transform, applications to partial differential equations. (Not open to students who have had MATH 133, 181, or 211.)

The first pair was recommended for EE and ECE majors specializing in Computer Engineering, Digital Systems, Signal Processing, or Systems and Robotics. The second pair was recommended for majors specializing in Solid-State Devices and Integrated Circuits, Electromagnetic Fields, Photonics, and other areas involving wave propagation in space and time, and for students who must choose a math option before they have made a specialization decision.

The MATH 107/108 pair is required for newly matriculating students (except dual majors in mathematics) and is strongly recommended for students who have not yet begun the MATH 104/131 or MATH 111/114 pairs.