LEC #  TOPICS  KEY DATES 

1  Sets, Set Operations, and Mathematical Induction  
2  Cantor’s Theory of Cardinality (Size)  Assignment 1 due 
3  Cantor’s Remarkable Theorem and the Rationals’ Lack of the Least Upper Bound Property  
4  The Characterization of the Real Numbers  Assignment 2 due 
5  The Archimedian Property, Density of the Rationals, and Absolute Value  
6  The Uncountabality of the Real Numbers  Assignment 3 due 
7  Convergent Sequences of Real Numbers  
8  The Squeeze Theorem and Operations Involving Convergent Sequences  Assignment 4 due 
9  Limsup, Liminf, and the BolzanoWeierstrass Theorem  
10  The Completeness of the Real Numbers and Basic Properties of Infinite Series  Assignment 5 due 
11  Absolute Convergence and the Comparison Test for Series  
12  The Ratio, Root, and Alternating Series Tests  Assignment 6 due 
Midterm Exam  Midterm Exam due  
13  Limits of Functions  
14  Limits of Functions in Terms of Sequences and Continuity  Assignment 7 due 
15  The Continuity of Sine and Cosine and the Many Discontinuities of Dirichlet’s Function  
16  The Min/Max Theorem and Bolzano’s Intermediate Value Theorem  Assignment 8 due 
17  Uniform Continuity and the Definition of the Derivative  
18  Weierstrass’s Example of a Continuous and Nowhere Differentiable Function  Assignment 9 due 
19  Differentiation Rules, Rolle’s Theorem, and the Mean Value Theorem  
20  Taylor’s Theorem and the Definition of Riemann Sums  Assignment 10 due 
21  The Riemann Integral of a Continuous Function  
22  The Fundamental Theorem of Calculus, Integration by Parts, and Change of Variable Formula  Assignment 11 due 
23  Pointwise and Uniform Convergence of Sequences of Functions  
24  Uniform Convergence, the Weierstrass MTest, and Interchanging Limits  Assignment 12 due 
25  Power Series and the Weierstrass Approximation Theorem  
Final Assignment  Final Assignment due 
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As Taught In:  Fall 2020 
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