Lectures for Mathematics 112, Fall 2023-24

Lectures for Mathematics 112, Fall 2023-24 (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 2.3 field axioms, 2.4 some of their consequences
W 9/6: Go over homework
F 9/8: [Add/section-change deadline] 2.5 Subtraction and division
M 9/11: Finish 2.5, start order
T 9/12: Go over homework, start 2.6 through 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: Discuss first exam; numerically unstable sequence; 4.1 the complexification of a field with no square root of -1
T 9/26: Skim 4.2 complex conjugate, start 5.1 sequences and binary search sequences
W 9/27: Go over homework, start binary search
F 9/29: More binary search, pth roots
M 10/2: [No-W drop deadline] Review the binary searches and their consequences, rational exponents
T 10/3: Go over homework, start chapter 6
W 10/4:
F 10/6: Go over homework
M 10/9: Through end of 6.3
T 10/10: Convergence, null sequences
W 10/11: Null sequences, convergence results through the reciprocal rule
F 10/12: Go over homework
Fall break week
M 10/23: Review sequence results; relation between area, circumference of the unit disk
T 10/24: Finite geometric sum informally and formally, rho^n->0 if 0<=rho<1, b^{1/n}->1 if b>0
W 10/25: Geometric series; translation; fake golden ratio sequence fraction
F 10/27: Real golden ratio sequence, monotonic sequence theorem, square root sequence
M 10/30: Review monotone convergence, more on the square root sequence, {n^(1/n)}
T 10/31: Start function limits and continuity
W 11/1: More continuity, start the limit of a function
F 11/3: Limit as continuous extension, derivative as limit, three subtle limits
M 11/6: [Withdraw/leave deadline] Review continuity and function limits
T 11/7: Intermediate Value Theorem; Extreme Value Theorem
W 11/8: Start derivatives
F 11/10: Derivative of the rational power function
M 11/13: Generative derivative rules
T 11/14: Chain rule
W 11/15: Start series: harmonic series diverges, nth term test, comparison test
F 11/17: p-test, {t^n/n!} summable, limit-comparison, ratio test
M 11/20: Alternating series test, absolute convergence test, start power series
T 11/21: Power series radius of convergence
W 11/22: Differentiation theorem
F 11/24: Thanksgiving Holiday
M 11/27: Review difference of powers formula, start specific power series examples
T 11/28: More power series examples
W 11/29: Power series trigonometry
F 12/1: Logarithm, arctangent, power function functions via power series
M 12/4: Geometry of exp(z)
T 12/5: No meeting (college on Thursday schedule)
W 12/6: Geometry of sine, zeta(s) for negative integers s

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