Math 142A: Notes
Fall 2021

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9/24/2021 (§1): Introduction to the course, number systems, mathematical induction
9/27/2021 (§1.2-1.3): Algebraic numbers, rational zeros theorem, properties of an ordered field, triangle inequality
9/29/2021 (§1.4-1.5): Triangle inequality, maximum, upper bound, completeness axiom
10/01/2021 (§1.4, 2.7): Archimedean property, denseness of Q, introduction to sequence convergence
10/04/2021 (§2.7-8): Sequence convergence
10/06/2021 (§2.9): Sequence boundedness, limits of sums and products
10/08/2021 (§2.9): Limit of a product = product of the limits, sequences that diverge to infinity
10/11/2021 (§2.10): Monotone convergence theorem, lim inf and lim sup
10/13/2021 (§2.10): More limsup and liminf, Cauchy sequences
10/15/2021 (§2.11): Subsequences
10/18/2021 (§2.11): Subsequential limits
10/20/2021 (§2.12): limsup and liminf of sums and products
10/22/2021 (§2.12): Ratio and root tests for sequences
10/25/2021 (§2.14): Introduction to series convergence
10/27/2021 (§2.14): Comparison test and ratio test
10/29/2021 (§2.14): More examples of the comparison test, root test, and ratio test
11/01/2021 (§2.15): Integral test and alternating series test
11/03/2021 (§2.14-2.15): Recap on computational series techniques
11/05/2021 (§3.17): Definition of function continuity
11/08/2021 (§3.17): Examples and properties of function continuity
11/10/2021 (§3.18): Extreme value theorem and intermediate value theorem
11/12/2021 (§3.18): Consequences of the intermediate value theorem and other properties about continuity
11/15/2021 (§3.19): Midterm 2 review, intro to uniform continuity
11/17/2021 (§3.19): Uniform continuity
11/19/2021 (§3.19): Uniform continuity
11/22/2021 (§3.20): lim_S f(x) (towards defining limit of a function at a point)
11/24/2021 (§3.20): Limits of functions
11/29/2021 (§3.20): Limits of functions (epsilon/ delta version)
12/01/2021 Chapter 3 review (plus a few extra short problems not seen in class)



Eva Belmont (ebelmont at ucsd.edu)