# Course Website

## Math 6301: Analysis I

**Lecture:** MATH 6301-100

**Room:** Morton Hall 313

**Time:** MWF 9:40am -- 10:35am

**Instructor:** Marcel Bischoff

**Office:** Morton Hall 521

**Office Phone:** (740-59)3-1261

**Office Hours:**
Mon & Wed: 10:45am-11:45am, Fri: 8:00-9:00am

### Schedule

- Mon 08/27:
- Syllabus
- Sets, Mappings, Equivalence relations
- Wed 08/29:
- Axiom of Choice, Zorn's Lemma
- Real Numbers
- Suggested Problem: Section 1.1, Problem 1.
- Fri 08/31:
- Section 1.1. and 1.2
- Natural Numbers, Mathematical Induction, Archimedean Property, Integers, Rational Numbers
- Suggested Problems: Section 1.1, 1.2
- Mon 09/03: Labor Day (no class)
- Wed 09/05:
- $\sqrt 2$ is not rational, $\mathbb Q$ is dense in $\mathbb R$
- Pigeonhole Principle, Cantor–Schröder–Bernstein Theorem, Countable Sets, Uncountable Sets
- Suggested Problems: Section 1.3
- Fri 09/07:
- $(a,b)$ is uncountable, Topological Space, Metric Space Topology, Every open set of $\mathbb R$ is a countable disjoint union of open intervals.
- Mon 09/10:
- Hand in: Homework 01
- Points of closure, Closure, Neighbourhoods, Compactness, Heine-Borel Theorem
- Wed 09/12:
- The Nested Set Theorem, Sigma-algebras, Borel Sets
- Convergent sequences are bounded, the Monotone Convergence Criterion for Real Sequences
- Suggested problems: Section 1.4
- Fri 09/14:
- Bolzano-Weierstrass Theorem, Cauchy sequence, Cauchy's convergence theorem, Linearity of the limit
- Quiz 01
- Mon 09/17:
- Limit superior and limit inferior, Series
- Suggested problems: Section 1.5
- Continuous Functions, Extreme Value Theorem
- Wed 09/19:
- Intermediate Value Theorem, Uniform Continuity, Heine-Cantor Theorem, Monotone Functions
- Suggested problems: Section 1.6
- Fri 09/21:
- Outer measure
- Quiz 02
- Suggested Problem: Section 2.1
- Mon 09/24:
- Hand in Homework 02
- Hand in Corrections of Quiz 01 if you are unhappy with your performance/score
- Lebesgue Measure
- The $\sigma$-algebra of Lebesgue measurable sets
- Suggested Problem: Section 2.2
- Wed 09/26:
- The $\sigma$-algebra of Lebesgue measurable sets
- Suggested Problems: Section 2.3
- Outer/inner approximation of Lebesgue measurable sets
- Fri 09/28:
- Outer/inner approximation of Lebesgue measurable sets
- Suggested Problems: Section 2.4
- Countable additivity of Lebesgue measure, Continuity of Lebesgue Measure
- Handed out: Homework 04
- Mon 10/01:
- Hand in Corrections of Quiz 02 if you are unhappy with your performance/score
- Wed 10/03:
- Cantor Set, Cantor-Lebesgue Function
- Slides
- Hand in Homework 03
- Fri 10/05: Reading Day: Class does not meet
- Mon 10/08:
- Cantor-Lebesgue Function, Lebesgue measurable functions
- Suggested Problems: Section 2.5, 2.6, 2.7
- Wed 10/10:
- Review
- Fri 10/12:
- Review
- Hand in Homework 04
- Mon 10/15: Midterm
- Wed 10/17:
- Fri 10/19:
- Suggested Problems: Section 3.1
- Mon 10/22:
- Suggested Problems: Section 3.2
- Simple Approximation
- Wed 10/24:
- Fri 10/26:
- Suggested Problems: Section 3.3
- Mon 10/29:
- Suggested Problems: Section 4.1
- Wed 10/31:
- Suggested Problems: Section 4.2
- Fri 11/02:
- Mon 11/05:
- Hand in Homework 05
- Suggested Problems: Section 4.3
- Wed 11/07:
- Suggested Problems: Section 4.4
- Fri 11/09:
- Mon 11/12:
- Wed 11/14:
- Fri 11/16:
- Mon 11/19:
- Wed 11/21: Thanksgiving
- Fri 11/23: Thanksgiving
- Mon 11/26:
- Wed 11/28:
- Fri 11/30:
- Mon 12/03:
- Wed 12/05:
- Fri 12/07:
- Fri 12/14: 8:00am-10am: Final Exam

### Ressources

- Tao - Analysis I (free eBook access through Alden Library)
- Tao - Analysis II (free eBook access through Alden Library)

Last update: 2018-11-16 17:03:54.