Ross Chapter 1

1. §1 The set N of Natural Numbers
2. §2 The set Q of Rational Numbers
3. §3 The Set R of Real Numbers
4. §4 The completeness Axiom

Link to Textbook Notes: midterm_1_ch_1.pdf

Ross Chapter 2

1. §7 Limits of Sequences
2. §9 Limit Therorems for Sequences
3. §10 Monotone Sequences and Cauchy Sequences
4. §11 Subsequences
5. §12 lim sup's and lim inf's
6. Exrta: Intro to Proofs

Link to Textbook Notes: midterm_1_ch_2.pdf

Rudin Ch.2, Ross §13

Rudin Ch.2 Basic Topology

1. Finite, Countable, and Uncountable Sets
2. Metric Spaces
3. Compact Sets
4. Perfect Sets
5. Connected Sets

Ross Ch 2. Sequences §13 *Some Topological Concepts in Metric Spaces

Link to Textbook Notes: rudin_ch_2_ross_13.pdf

Ross Ch 2. Sequences

1. §14 Series
2. §15 Alternating Series and Integral Tests

Link to Textbook Notes: ross_14_15.pdf

Rudin Ch. 4 Continuity

1. Limits of Functions
2. Continuous Functions
3. Continuity and Compactness
4. Continuity and Connectedness
5. Discontinuities
6. Montotonic Functions
7. Infinite Limits and Limits at Infinity

Link to Textbook Notes: rudin_ch_4.pdf

Ross Ch. 4 §24, §25, §26; Rudin Ch. 7 (sections 1-2)

Ross Ch. 4 - Sequences and Series of Functions

1. §24 Uniform Convergence
2. §25 More on Uniform Convergence
3. §26 Differentiation and Integration of Power Series

Rudin Ch. 7 - Sequences and Series of Functions

1. Uniform Convergence
2. Uniform Convergence and Continuity

Link to Textbook Notes: ross_24_25_26_rudin_7.pdf