Lectures for Mathematics 112, Fall 2017-18 (tentative)

• M 8/28: Overview
• T 8/29: Skim through Ch1
• W 8/30: Start 2.1: Binary operators, identity, inverses, associativity
• F 9/1: Go over homework

• M 9/4: Labor Day Holiday
• T 9/5: Continue through field axioms, some of their consequences
• W 9/6: Go over homework

• M 9/11: Finish 2.5, start order
• T 9/12: Go over homework, start inequalities
• W 9/13: Finish inequalities, start absolute value
• F 9/15: Finish absolute value; inductive sets, the natural numbers of a field

• M 9/18: Induction theorem, addition and multiplication in the integers of a field, no natural number between 0 and 1
• T 9/19: Least Integer Principle; no square root of 2 in the rational field
• W 9/20: Recursive definitions, a^{m+n} = a^m a^n for all natural n,m, go over homework
• F 9/22: The integers and rational numbers of a field; finish 3.3

• M 9/25: 3.4; skim 3.5; Catalan numbers by grid; pirates
• T 9/26: 4.1
• W 9/27: Go over homework, start binary search
• F 9/29: More binary search

• M 10/2: [No-W drop deadline] More binary search, finish 5.2
• T 10/3: Go over homework, most of 5.3
• W 10/4: Redo pth roots, rational exponents
• F 10/6: Go over homework, start complex numbers

• M 10/9: Through end of 6.3
• T 10/10: Rest of Ch6; picture of stereographic projection
• W 10/11: 7.1, go over homework
• F 10/12: Convergence, null sequences, dull sequences

• Fall break week

• M 10/23: More null sequences
• T 10/24: Results on null sequences
• W 10/25: Convergence results through the reciprocal rule
• F 10/27: Preview homework; start geometric series

• M 10/30: Geometric series; translation; golden ratio as continued fraction
• T 10/31: Quote {n^{1/n}}->1; start continuity
• W 11/1: Most of 8.2
• F 11/3: Start limit of a function

• M 11/6: [Withdraw/leave deadline] Limit of a function; start Ch9
• T 11/7: Intermediate Value Theorem; Extreme Value Theorem
• W 11/8: Start derivatives
• F 11/10: Chain rule; start 10.2

• M 11/13: Finish 10.2 up to 10.31; skim 10.3
• T 11/14: Start series: nth term test, harmonic series diverges
• W 11/15: p-test, comparison test, {t^n/n!} summable
• F 11/17: Limit-comparison, ratio test, alternating series test

• M 11/20: go over homework, Taylor series I
• T 11/21: Taylor series II
• W 11/22: Taylor series III, go over homework
• F 11/24: Thanksgiving Holiday

• M 11/27: Power series, radius of convergence
• T 11/28: Differentiation theorem; start exp(z)
• W 11/29: More on the exponential function
• F 12/1: Exponential and trigonometric functions via power series

• M 12/4: Geometry of exp(z)
• W 12/6: Geometry of sine, zeta(s) for negative integers s