## 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`)