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
  • F 9/8: [Add/section-change deadline] Subtraction and division

  • 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: Absolute convergence implies convergence, go over homework, 18th century calculation
  • T 11/21: Power series, radius of convergence
  • W 11/22: Differentiation theorem; start exp(z)
  • F 11/24: Thanksgiving Holiday

  • M 11/27: More on the exponential function
  • T 11/28: Exponential and trigonometric functions via power series
  • W 11/29: Geometry of exp(z)
  • F 12/1: Geometry of sine, zeta(s) for negative integers s

  • M 12/4: Series for cotangent; cos(72deg)
  • W 12/6: Comments on the Differentiation Theorem, summary

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