![]() There is a mix of proofs, calculations, and applications with the emphasis depending somewhat on the instructor. Math 419 covers much of the same ground as Math 417 but presents the material in a somewhat more abstract way in terms of vector spaces and linear transformations instead of matrices. Math 417 and Math 419 may not be used as electives in the Statistics major. No credit granted to those who have completed or are enrolled in Math 420. Credit is granted for only one course among Math 214, 217, 417, and 419. Applications include linear networks, least squares method (regression), discrete Markov processes, linear programming, and differential equations.ģ credits. Topics include matrix operations, echelon form, general solutions of systems of linear equations, vector spaces and subspaces, linear independence and bases, linear transformations, determinants, orthogonality, characteristic polynomials, eigenvalues and eigenvectors, and similarity theory. This course is not intended for mathematics majors, who should elect Math 217, and/or Math 493-494 if pursuing the honors major. Diversity rather than depth of applications is stressed. The main emphasis is on concepts and problem-solving, but students are responsible for some of the underlying theory. This course is an introduction to the properties of and operations on matrices with a wide variety of applications. Many problems in science, engineering, and mathematics are best formulated in terms of matrices - rectangular arrays of numbers. No credit granted to those who have completed or are enrolled in Math 214, 217, 419, or 420. Three mathematics courses beyond Math 110ģ credits. The course often includes a section on abstract complexity theory including NP completeness. Algorithm types such as divide-and-conquer, backtracking, greedy, and dynamic programming are analyzed using mathematical tools such as generating functions, recurrence relations, induction and recursion, graphs and trees, and permutations. Typical problems considered are: sorting, searching, matrix multiplication, graph problems (flows, traveling salesman), and primality and pseudo-primality testing (in connection with coding questions). Different instructors will put varying degrees of emphasis on mathematical proofs and computer implementation of these ideas. The goal here is to develop the mathematical tools necessary to analyze such algorithms with respect to their efficiency (running time) and correctness. Students entering Math 416 typically have encountered some of these problems and their algorithmic solutions in a programming course. Many common problems from mathematics and computer science may be solved by applying one or more algorithms - well-defined procedures that accept input data specifying a particular instance of the problem and produce a solution. Math 312, 412 or EECS 280 and Math 465 or permission of instructor Notions such as generator, subgroup, direct product, isomorphism, and homomorphism are defined and studied. These structures are presented as abstractions from many examples such as the common number systems together with the operations of addition or multiplication, permutations of finite and infinite sets with function composition, sets of motions of geometric figures, and polynomials. These are then applied to the study of particular types of mathematical structures: groups, rings, and fields. The initial topics include ones common to every branch of mathematics: sets, functions (mappings), relations, and the common number systems (integers, rational numbers, real numbers, complex numbers). Math 217, or equivalent, required as background. Much of the reading, homework exercises, and exams consist of theorems (propositions, lemmas, etc.) and their proofs. Although the topics discussed here are quite distinct from those of calculus, an important goal of the course is to introduce the student to this type of analysis. A typical student entering this course has substantial experience in using complex mathematical (calculus) calculations to solve physical or geometrical problems, but is inexperienced at analyzing carefully the content of definitions and the logical flow of ideas which underlie and justify these calculations. ![]() ![]() This course is designed to serve as an introduction to the methods and concepts of abstract mathematics.
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