math 112 introduction to analysis // spring 2018
MWF 12:00--12:50 Library 204
MWF 2:40--3:30 Library 389
Office Hours: M 1:00--2:30, W 1:00--2:30, Th 3:00--4:30; also by appointment
Math Help Center: SuMTWTh 19:00--21:00, in Library 389
Math 112 Help Sessions: M and Th, 6:00--7:00 in L204
Syllabus
Getting started with LaTeX
A guide to mathematical writing
Class handout on complete ordered fields
Class handout on series tests
Review sheet for the final exam
- Week 1
- M 1/22: course intro, mathematical statements, proof by induction
- Reading: § 1.1 (skim), 1.5
- W 1/24: proof by induction
- Reading: § 1.4, 1.5
- F 1/26: negation of statements, intro to set theory
- Reading: § 1.2, 1.3 (skim), 2.1
- HW #1 DUE (tex)
- Week 2
- M 1/29: intersection, union, and complement
- Reading: § 2.1
- T 1/30: HW #2 DUE (tex)
- W 1/31: cartesian product, equivalence relations
- Reading: § 2.2, 2.3
- F 2/2: equivalence relations
- Reading: § 2.3
- HW #3 DUE (tex)
- Week 3
- M 2/5: functions
- Reading: § 2.4
- T 2/6: HW #4 DUE (tex)
- W 2/7: injective, surjective, and bijective functions
- Reading: § 2.4
- F 2/2: composition of functions and inverses
- Reading: § 2.4
- HW #5 DUE (tex)
- Week 4
- M 2/12: binary operations
- Reading: § 2.5
- T 2/13: HW #6 DUE (tex)
- W 2/14: fields
- Reading: § 2.6
- F 2/16: ordered fields
- Reading: § 2.7
- HW #7 DUE (tex)
- Week 5
- M 2/19: complete ordered fields
- Reading: § 2.9
- T 2/20: HW #8 DUE (tex)
- W 2/21: R is the unique complete ordered field
- Reading: § 2.9, 2.10
- F 2/16: in-class MIDTERM EXAM (practice questions, solutions)
- Week 6
- M 2/19: absolute values and the triangle inequality
- Reading: § 2.10
- T 2/20: HW #9 DUE (tex)
- W 2/21: complex numbers
- Reading: § 3.1, 3.2
- F 3/2: the geometry of complex numbers
- Reading: § 3.3, 3.4
- HW #10 DUE (tex)
- Week 7
- M 3/5: the geometry of complex numbers
- Reading: § 3.4
- T 3/6: HW #11 DUE (tex)
- W 3/7: open and closed sets; the topology on R and C
- Reading: § 3.5
- F 3/9: sequences
- Reading: § 8.1, 8.2
- HW #12 DUE (tex)
Spring Break
- Week 8
- M 3/19: epsilon-N proofs
- Reading: § 8.2, 8.3
- T 3/20: HW #13 DUE (tex)
- W 3/21: the limit theorems
- Reading: § 8.3, 8.4
- F 3/23: divergence of sequences, the squeeze theorem
- Reading: § 8.3, 8.4
- HW #14 DUE (tex)
- Week 9
- M 3/26: the squeeze theorem, bounded sequences
- Reading: § 8.4, 8.6
- T 3/27: HW #15 DUE (tex)
- W 3/28: bounded sequences and the monotone convergence theorem
- Reading: § 8.6
- F 3/30: subsequences and Cauchy sequences
- Reading: § 8.7, 8.8
- HW #16 DUE (tex)
- Week 10
- M 4/2: infinite series
- Reading: § 9.1
- T 4/3: HW #17 DUE (tex)
- W 4/4: geometric series, harmonic series [handout: series tests]
- Reading: § 9.1
- F 4/6: convergence theorems for series TAKE-HOME MIDTERM EXAM DISTRIBUTED (practice questions)
- Reading: § 9.2
- HW #18 DUE (tex)
- Week 11
- M 4/9: practice with convergence tests for series TAKE-HOME MIDTERM DUE IN-CLASS
- Reading: § 9.2
- T 4/10: no HW!
- W 4/11: limits of functions
- Reading: § 4.1, 4.2, 4.3
- F 4/13: continuity and derivatives
- Reading: § 5.1, 6.1, 6.2
- HW #18 DUE (tex)
- Week 12
- M 4/16: Taylor approximation
- Reading: § 5.2, 5.3
- T 4/17: HW #19 DUE (tex)
- W 4/18: power series and their radius of convergence
- Reading: § 6.3, 6.5
- F 4/20: two theorems about power series
- Reading: § 9.3, 9.4
- HW #20 DUE (tex)
- Week 13
- M 4/23: Euler's formula
- Reading: § 9.7, 9.8
- T 4/24: HW #19 DUE (tex)
- W 4/25: more on power series
- Reading: § 9.8
- F 4/27: advanced topics in topology; no HW!
FINAL EXAM: Wednesday, May 9, 6pm--9pm, Vollum Lecture Hall