MATH 3110 is a transition from calculus to real analysis. We will give a rigorous treatment of concepts encountered in calculus. Emphasis will be placed on understanding and constructing mathematical proofs.

Textbooks

The course text is Introduction to Analysis by Arthur Mattuck. If you do not have the book yet, please consult the book's webpage, which has the first couple of chapters available.

Announcements

• (11/22): Here are the solutions to the second prelim exam.
• (11/15): The last two homeworks will have the following due dates: HW 11 will be due on Tuesday, November 22 and HW 12 will be due on Thursday, December 1, the last day of class.
• (11/01): The second prelim will be in-class on Tuesday, November 15.
• (10/13): Here are the solutions to the first prelim exam.
• (10/04): The Homework 6 due date has been postponed to Thursday, October 13, due to fall break. Homework 7 (which will be posted next week) will be due on Tuesday, October 18.
• (09/20): The first prelim will be in-class on Tuesday, October 4.
• (09/10): Yujia will be out of town and so will not have her office hours on September 12 or 19.
• (09/09): (Public Service Announcement) For the first part of HW 3, Problem 6, make sure your calculator is in radians.
• (09/03): Due to Malott Hall being closed for Labor Day, the HW 2 due date has been postponed to Thursday, and your TAs will have office hours as follows: Yujia's will be from 4:30-6:30pm on Tuesday and Ziyi's will be from 12:40-2:40pm on Wednesday.
• Here are the syllabus and the questionnaire that were passed out on the first day.
• The first class takes place on Tuesday, August 23.

Homeworks

• Homework 1, due Tuesday, August 30, Solutions
• Homework 2, due Tuesday, September 6 (postponed to Thursday), Solutions
• Homework 3, due Tuesday, September 13, Solutions.
• Homework 4, due Tuesday, September 20, Solutions.
• Homework 5, due Tuesday, September 27, Solutions.
• Prelim 1 Practice Problems. These will not be graded or collected.
• Homework 6, due Thursday, October 13, Solutions.
• Homework 7, due Tuesday, October 18, Solutions.
• Homework 8, due Tuesday, October 25, Solutions.
• Homework 9, due Tuesday, November 1, Solutions.
• Homework 10, due Tuesday, November 8, Solutions.
• Prelim 2 Practice Problems. These will not be graded or collected.
• Homework 11, due Tuesday, November 22, Solutions.
• Homework 12, due Thursday, December 1, Solutions.

Topics covered

• Week 1: Why do I need to know analysis?, Sequences (Ch. 1, 2)
• Week 2: Inequalities, approximations, and limits of sequences (Ch. 2, 3, 4, 5)
• Week 3: Error terms, properties of sequences, completeness and the Cauchy criterion for convergence (Ch. 4, 5, 6).
• Week 4: Completeness for sets, lim sup and lim inf, infinite series and power series (Ch. 6, 7, 8).
• Week 5: Functions, limits and continuity (Ch. 9, 10, 11).
• Week 6: Limits of functions, one-sided limits, and infinite limits, points of discontinuity (Ch. 11), midterm review.
• Week 7: Prelim exam 1, Bolzano's theorem, the Intermediate Value Theorem, and applications (Ch. 12).
• Week 8: Continuous functions on compact intervals: Boundedness Theorem and Extreme Value Theorem (Ch. 13).
• Week 9: Uniform continuity, Differentiation (Ch. 13, 14, 15).
• Week 10: Optimization, convex/concave functions, Riemann integration, Taylor approximation (Ch. 16, 17, 18, 19).
• Week 11: Fundamental Theorems of Calculus, relations between differentiation and integration, improper integrals (Ch. 20, 21).
• Week 12: Approximations, precision, and introduction to sequences and series of functions, midterm II review (Ch. 22).
• Week 13: Prelim exam 2, more on sequences and series of functions (Ch. 22).
• Week 14: Integration and differentiation of limits of sequences and series of functions (Ch. 22).
• Week 15: Infinite sets, measure zero sets, and Lebesgue integration (Ch. 23).

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