# Duke Math 431, Advanced Calculus I, Spring 2015

Email: henry dot adams at colostate dot edu

Lectures: MWF 3:20-4:10pm in Gross Hall 304B
Textbook: Fundamental Ideas of Analysis by Michael Reed
List of typos

Overview: This course is a proof-based introduction to elementary mathematical analysis. Topics covered include cardinality of sets, convergence of sequences, continuous functions, the Riemann integral, differentiation, sequences of functions, metric spaces, and completeness. Students will learn how to write rigorous mathematical proofs and how to construct counterexamples.

Syllabus: Here is the course syllabus.

## Homework

Homework 1 is due Friday, January 16.
Homework 2 is due Friday, January 23.
Homework 3 is due Friday, January 30.
Homework 4 is due Friday, February 6.
Homework 5 is due Friday, February 13.
Homework 6 is due Friday, February 27.
Homework 7 is due Friday, March 6.
Homework 8 is due Friday, March 20.
Homework 8.5 is not to be turned in or graded.
Homework 9 is due Friday, April 3.
Homework 10 is due Friday, April 10.
Homework 11 is due Friday, April 17.
Homework 12 is not to be turned in or graded.

All homework is due at the beginning of class. Solutions will be posted on Sakai.

## Exams

Here is a Practice Midterm 1, posted February 9.
Here are Solutions to Practice Midterm 1, posted February 10.
Here is a Midterm 1, taken February 16.
Here are Solutions to Midterm 1, posted February 18.
Here is a Practice Midterm 2, posted March 21.
Here are Solutions to Practice Midterm 2, posted March 24.
Here is a Midterm 2, taken March 27.
Here are Solutions to Midterm 2, posted March 28.
Here is a Practice Final, posted April 19.
Here are Solutions to the Practice Final, posted April 21.

## Notes

A proof that zero is less than one, posted January 15.
Why is the definition of two sets having the same cardinality symmetric?, posted January 23.
Proof of Theorem 2.2.6, posted January 31.
Proof of Corollary 3.3.6, posted February 25.
Lipschitz vs uniform continuity, posted March 24.

## Schedule

 Date Text Remark Jan 7 §1.1 Jan 9 §1.1, §1.2 Jan 12 §1.2 Jan 14 §1.3 Jan 16 §1.3, §1.4 Homework 1 due Jan 19 MLK Day Jan 21 §1.4 Drop/add ends Jan 23 §2.1 Homework 2 due Jan 26 §2.1, §2.2 Jan 28 §2.2 Jan 30 §2.4 Homework 3 due Feb 2 §2.4, §2.5 Feb 4 §2.5, §2.6 Feb 6 §2.6 Homework 4 due Feb 9 §3.1 and Review Feb 11 §3.1 and Review Feb 13 Review Homework 5 due Feb 16 Midterm #1 Midterm through §2.6 Feb 18 §3.1 Feb 20 §3.2 Feb 23 §3.2, §3.3 Feb 25 §3.3, §4.1 Feb 27 §4.1 Homework 6 due Mar 2 §4.2 Mar 4 §4.3 Mar 6 §4.3, §4.5 Homework 7 due Spring Break, March 9-13 Mar 16 §4.5 Mar 18 §5.1 Mar 20 §5.1, §5.2 Homework 8 due Mar 23 §5.2 Mar 25 Review Last day to withdraw Mar 27 Midterm #2 Midterm through §4.5 Mar 30 §5.3 Apr 1 §5.3, §5.6 Apr 3 §5.6 Homework 9 due Apr 6 §5.7 Apr 8 §5.7, §6.1 Apr 10 §6.1 Homework 10 due Apr 13 §6.2 Apr 15 §6.2 Apr 17 Review and class picture Homework 11 due Apr 20 Review Apr 22 Review Final Exam, Thursday April 30, 2:00-5:00pm