Undergraduate Program Pure Mathematics The Pure Mathematics Program is designed to provide broad training in basic modern mathematics including an introduction to the methods of rigorous mathematical proof and exposure to the major areas: Algebra, Analysis, and Geometry/Topology. Prerequisite to concentration in Pure Mathematics is one of the sequences 215-217, 255-217, 285-217, or 395-396.  Note that Math 216 is not intended for mathematics concentrators.  Students who have completed one of the sequences 255-256 or 285-286 may substitute Math 513 for Math 217. All Pure Mathematics concentrators are also strongly encouraged to take Physics 140-141 and 240-241 and to acquire a working knowledge of a high-level computer language (e.g. Fortran, C, or C++) at a level equivalent to the completion of EECS 183. The concentration program must include at least nine courses: II. four basic courses, III. four elective courses, and IV. one cognate course as described below. The basic courses consist of one from each of the following groups completed with a grade of at least C-.    Modern Algebra: Math 412 or 512    Differential Equations: Math 256, 286, or 316    Analysis: Math 351 or 451    Geometry/Topology: Math 433, 490, 531, 532, or 590 More advanced students, such as those who have completed Math 396, may substitute higher lever courses with the approval of a concentration advisor. Following Math 215 all students intending to concentrate in Pure Mathematics should elect Math 217 (Linear Algebra) rather than Math 216 (Introduction to Differential Equations). Math 216 is not intended for mathematics concentrators, who generally take Math 316 (Differential Equations) after completing Math 217. The four elective courses must be chosen in consultation with an advisor to provide a cohesive program which explores an area of mathematics in some depth. There is a good deal of freedom here, but a random selection of courses will not satisfy this requirement. The courses should be chosen from the following list or have course number 600 or above. Math 288 and 289 are repeatable 1-credit courses and can be used to satisfy the elective requirement only in combinations totaling 3 credits. 288 Math Modeling Workshop 289 Problem Solving 354 Fourier Analysis and its App. 362 App. of Calculus and Linear Algebra 404 Inter. Diff. Equations 416 Theory of Algorithms 420 Matrix Algebra II 423 Mathematics of Finance 425 Introduction to Probability 432 Projective Geometry 433 Intro. to Differential Geometry 450 Adv. Mathematics for Engineers I 452 Advanced Calculus II 454 Boundary Value Prob. for PDE 462 Mathematical Models 463 Mathematical Modeling in Biology 464 Inverse Problems 471 Introduction to Numerical Methods 475 Elementary Number Theory 481 Introduction to Mathematical Logic 490 Introduction to Topology 498 Topics in Modern Mathematics 525 Probability Theory 531 Transformation Groups in Geom. 532 Topics Discr. & Appl. Geom. 535 Intro. to Algebraic Curves 537 Intro. to Diff. Manifolds 550 Intro. to Adaptive Systems 555 Intro. to Complex Variables 556 Methods of Applied Mathematics I 557 Methods of Applied Math. II 558 Ordinary Differential Equations 559 Topics in Applied Mathematics 561 Linear Programming I 562 Continuous Optimization Meth. 563 Advanced Mathematical Biology 565 Combinatorics and Graph Theory 567 Intro. to Coding Theory 571 Numer. Meth. for Sci. Comput. I 572 Numer. Meth. for Sci. Comput. II 575 Intro. to Theory of Numbers 582 Introduction to Set Theory 590 An Intro. to Topology 591 General & Diff. Topology 592 An Intro. to Algebraic Topology 593 Algebra I 594 Algebra II 596 Analysis I (Complex) 597 Analysis II (Real)   One cognate course should be chosen from some field other than mathematics.  Almost any field is acceptable, but the course must be at the 300+ level and should have significant mathematical content, at least at the level of Math 215.  A list of suggested courses is available in the Undergraduate Program office, but in all cases approval of a concentration advisor is required.