208 / FIELDS OF INSTRUCTION


in all doctoral programs, the latter for three quarters. Descriptions of the
500-level courses are to be found in the undergraduate catalog. Each doctoral
candidate is required to take two advanced-level courses for which at least one
of the basic advanced courses is a prerequisite. Doctoral candidates must pass
reading knowledge examinations in two of the following foreign languages:
French, German, or Russian.
 Advanced mathematics courses are not necessarily numbered according
 to their difficulty. The 700 courses are those related more specifically to
 some particular field. Much of the advanced graduate training is done in MS
 690. In recent years eight or more sections of 690 have been offered each
 quarter.
 Every graduate student is expected to attend the regular colloquium.
 Details concerning all requirements for graduate degrees in mathematics
 can be obtained by writing to the Mathematics Department Graduate Selection
 Committee.
 COURSES FOR ADVANCED UNDERGRADUATES AND GRADUATES
 MS 501--INTERMEDIATE DIFFERENTIAL EQUATIONS FOR ENGINEERS AND
 PHYSICAL SCIENTISTS. 3 credits
MS 502-VECTOR ANALYSIS. 3 credits
MS 503-INTRODUCTION TO COMPLEX VARIABLES FOR ENGINEERS AND
 PHYSICAL SCIENTISTS 1. 3 credits
MS 504--INTRODUCTION TO COMPLEX VARIABLES FOR ENGINEERS AND
 PHYSICAL SCIENTISTS 2. 3 credits
MS 505-INTRODUCTION TO PARTIAL DIFFERENTIAL EQUATIONS. 3 credits
MS 507-FOURIER SERIES AND TRANSFORMS 1. 4 credits
MS 508-FOURIER SERIES AND TRANSFORMS 2. 4 credits
MS 509-INTRODUCTION TO FUNCTIONAL ANALYSIS 1. 4 credits
MS 510-INTRODUCTION TO FUNCTIONAL ANALYSIS 2. 4 credits
MS 531-INTRODUCTORY ALGEBRA 1. 3 credits
MS 532-INTRODUCTORY ALGEBRA 2. 3 credits
MS 533-INTRODUCTORY ALGEBRA 3. 3 credits
MS 535-COMPUTABILITY AND UNSOLVABILITY. 5 credits
MS 541-MODERN ANALYSIS 1. 3 credits
MS 542-MODERN ANALYSIS 2. 3 credits
MS 543-MODERN ANALYSIS 3. 3 credits
MS 544-THEORY OF DIFFERENTIAL EQUATIONS 1. 3 credits
MS 545-THEORY OF DIFFERENTIAL EQUATIONS 2. 3 credits
MS 547-ADVANCED CALCULUS 1. 3 credits
MS 548-ADVANCED CALCULUS 2. 3 credits
MS 549-ADVANCED CALCULUS 3. 3 credits
MS 551-PROSEMINAR 1. 4 credits
MS 552-PROSEMINAR 2. 4 credits
MS 553-PROSEMINAR 3. 4 credits
MS 555-INTRODUCTION TO ANALYTIC FUNCTIONS 1. 3 credits
MS 556-INTRODUCTION TO ANALYTIC FUNCTIONS 2. 3 credits
MS 561-INTRODUCTION TO TOPOLOGY 1. 3 credits
MS 562-INTRODUCTION TO TOPOLOGY 2. 3 credits