Math 3100 - Introduction to Analysis - Spring 2021

 Syllabus Vanderbilt Math Club Putnam Competition

Schedule:
 Date Material covered Book section Assignment January 25 Introduction/sets/functions 0.1 and 0.2 Assignment Zero tex and pdf January 27 Natural numbers/induction 0.3 Assignment 1 - Due February 3rd, tex and pdf January 29 Countable sets 0.4 February 1 Real numbers 0.5 February 3 Sequences 1.1 Assignment 2 - Due February 10th, tex and pdf February 5 Cauchy sequences 1.2 February 8 Operations with sequences 1.3 February 10 Subsequences I 1.4 Assignment 3 - Due February 17th, tex and pdf February 12 Subsequences II 2.1 February 15 Limits of functions 2.2 February 17 Operations with limits 2.3 February 19 Continuity 3.1 February 22 Algebra of continuous functions 3.2 February 24 Uniform continuity 3.3 Assignment 4 - Due March 3rd, tex and pdf February 26 Special topic I Exam 1 - Due February 26th by 6pm Central time, tex and pdf (Solutions) March 1 Compact sets 3.3 March 3 Properties of continuous functions 3.4 March 5 Properties of continuous functions II 3.4 Assignment 5 - Due March 12th, tex and pdf March 8 The derivative of a function 4.1 March 10 Operations with derivatives 4.2 March 12 Mean value theorem 4.3 Assignment 6 - Due March 17th, tex and pdf March 15 Mean value theorem II 4.3 March 17 L'Hospital's rule 4.4 March 19 The Riemann Integral 5.1 March 22 Integrable functions 5.2 March 24 Riemann sums 5.3 March 26 Special topic II Exam 2 due March 26th by 6pm Central time, tex and pdf (Solutions) March 29 The Fundamental Theorem of Integral Calculus 5.4 March 31 The algebra of integrable functions 5.5 April 2 Derivatives of integrals 5.6 Assignment 7 - Due April 9th, tex and pdf April 5 Change of variables 5.6 April 7 Change of variables II 5.7 April 9 Convergence of series 6.1 April 12 Absolute convergence 6.2 April 14 Ratio and root test 6.3 April 16 Conditional convergence 6.4 April 19 Power series 6.5 April 21 Taylor series 6.6 April 23 Special topic III Exam 3 due April 23rd by 6pm Central time, tex and pdf April 26 Convergence of functions 7.1 April 28 Uniform convergence 7.2 April 28 Uniform convergence of power series 7.3 Final Exam due May 10th by 6pm Central time, No late work accepted, tex and pdf