UC Berkeley Math 104: Course schedule

Course schedule

Lecture	Date	Topic	Reading	Notes
1	Jan 18	Natural numbers, mathematical induction	1
2	Jan 20	Field axioms and rational numbers	2
3	Jan 23	The completeness axiom	3, 4
4	Jan 25	Infinity	5
5	Jan 27	Sequences, convergence	7, 8	HW 1 due
6	Jan 30	Properties of sequences	9
7	Feb 1	Cauchy sequences	10
8	Feb 3	Subsequences	11	HW 2 due
9	Feb 6	Bolzano–Weierstraß theorem	11
10	Feb 8	lim sup and lim inf	12
11	Feb 10	Series and convergence properties	14	HW 3 due
12	Feb 13	Integral tests	15
13	Feb 15	Metric spaces: metrics	13, Ru2
14	Feb 17	Metric spaces: set topology	13, Ru2	HW 4 due
	Feb 20	Presidents Day
15	Feb 22	Metric spaces: compactness	13, Ru2
	Feb 24	Midterm 1
16	Feb 27	Continuity	17
17	Feb 29	Intermediate Value Theorem	18
18	Mar 2	Uniform continuity	19	HW 5 due
19	Mar 5	Limits of functions 1	20
20	Mar 7	Limits of functions 2	20
21	Mar 9	Power series 1	23	HW 6 due
22	Mar 12	Uniform convergence	24
23	Mar 14	Power series 2	25
24	Mar 16	Weierstraß approximation theorem	27	HW 7 due
25	Mar 19	Midterm review
	Mar 21	Midterm 2
26	Mar 23	Differentiation	28
	Mar 26	Spring Break
	Mar 28	Spring Break
	Mar 30	Spring Break
27	Apr 2	Mean Value Theorem / Rolle's theorem	29
28	Apr 4	Differentiation of power series	26, Ru7
29	Apr 6	L'Hôpital's rule	30	HW 8 due
30	Apr 9	Taylor's theorem	31
31	Apr 11	Riemann integration	32
32	Apr 13	Integration properties	33	HW 9 due
33	Apr 16	Fundamental theorem of calculus	34	See note 3
34	Apr 18	Fundamental theorem of calculus 2	34	See note 3
35	Apr 20	Improper integrals	36, 37	HW 10 due
36	Apr 23	Metric spaces: continuity	21
37	Apr 25	Metric spaces: continuity 2	21
38	Apr 27	Metric spaces: connectedness	22	HW 11 due

The numbers in the reading column correspond to the chapters in Elementary Analysis: The Theory of Calculus by Kenneth Ross.
Numbers in the reading column with “Ru” before them correspond to chapters in Principles of Mathematical Analysis by Walter Rudin. This book will be used to supplement the material in the main textbook. However, it is not necessary for you to have a copy of this, and all relevant information will be presented in the lectures.
The lectures on April 16th and April 18th will be given by Benjamin Stamm.