Instructor: Florent Baudier
Lectures: In College Station: typically MTWRF 8:30-11:45 a.m. in BLOC 605AX
In Besançon: typically MTWRF 9-11 a.m. in room 309B
Office hours: By appointment. Course description: Axioms of the real number system; point set theory of the real number line; compactness, completeness and connectedness; continuity and uniform continuity; sequences, series; theory of Riemann integration. A main goal of the course, essential to mastering the indicated material, is to learn how to apply precise mathematical reasoning in reading, understanding, and writing proofs of theorems in analysis. Textbook: Brian S. Thomson, Judith B. Bruckner, and Andrew M. Bruckner, Elementary Real Analysis, Second Edition (2008), Volume One. The course material is contained in Chapters 1, 2, 4, 5, 7, and 8 and is available for free download. Lecture Notes:
Lecture notes Homeworks:
Practice problem set 1 Practice problem set 1 solutions
Practice problem set 2 Practice problem set 2 solutions
Practice problem set 3 Practice problem set 3 solutions
Practice problem set 4 Practice problem set 4 solutions
Exams: Solution key Midterm Schedule:

Monday	Tuesday	Wednesday	Thursday	Friday
REVIEW sets, functions, induction principles, REAL NUMBERS commutative ordered field structure, the absolute value	least upper bound property, density of the rationals in the reals	Quiz #1 SEQUENCES OF REAL NUMBERS, convergence, uniqueness of the limit, boundedness, monotone convergence theorem	arithmetic of limits, comparison theorems	Quiz #2 subsequences, Bolzano-Weirstrass theorem

Monday	Tuesday	Wednesday	Thursday	Friday
Memorial day, no class, reading day	Quiz #3 Cauchy sequences, divergent sequences	Quiz #4 sequential closedness, sequential compactness, sequential Heine-Borel theorem	LIMITS OF FUNCTIONS two sided limits, manipulations of limits, comparison theorems	MIDTERM

Monday	Tuesday	Wednesday	Thursday	Friday
transfer to France, no class	orientation day in Besançon no class	CONTINUITY OF FUNCTIONS local continuity, Intermediate Value Theorem	Quiz #5 Extreme Value Theorem	Quiz #6 uniform continuity

Monday	Tuesday	Wednesday	Thursday	Friday
Quiz #7 DIFFERENTIABILITY local differentiability, local extrema	rules of differentiation	Quiz #8 Mean Value Theorem	reading day	L'Hôpital's rules

Monday	Tuesday	Wednesday	Thursday	Friday
Quiz #9 monotonicity and global differentiability	Quiz #10 RIEMANN INTEGRATION continuity and integrability, Fundamental Theorem of Calculus	FINAL REVIEW	reading day	FINAL EXAM