Instructor Office:  694 PGH
Office Hours: Mon 1-2, Wed 11-12 or by appointment
Phone Number:  513-7443
E-mail address:  dlabate@math.uh.edu
Homepage:  http://www.math.uh.edu/~dlabate

This is the first rigorous theorem/proof-type course in analysis at the University of Houston and seves to prepare students for advanced mathematics, especially the math courses in analysis numbered 3334 and higher. The aim of the course is to teach students mathematical reasoning and the construction of proofs in the environment of Real Numbers. During this course, students will develop their ability to think deductively, analyze mathematical statements, and apply mathematical ideas to the solution of new problems. The material covered during the course is centered on the theory underpinning one-dimensional calculus, and includes the concepts of real number system, function, limit, continuity, differential and integral calculus.
Please, notice that the emphasis of this course is on MATHEMATICAL PROOFS rather than calculus-type problems.

Analysis with an Introduction to Proof, Fifth Edition, by Steven R. Lay, Prentice-Hall, 2013 (the Fourth edition, 2004, is also acceptable)
 

I encourage you to work the homework assignments regularly and carefully. The only way to learn how to write proofs (and hence truly understand the mathematical concepts involved) is by working on your own, and not by watching someone else doing the work for you. Homework assignemnts will require for you to write simple proofs based on the material of the lectures. You are encouraged to discuss the homework with other students or with me (preferably in my office). However, you should be able to work on your own to master the material and be able to solve the test problems in class. Every week I will collect the homework and/or administer a short quiz (10 min) based on the homework. The quiz will be at the beginning of the lecture and the homework is due on the DUE DATE AT THE BEGINNING OF THE LECTURE (12:05PM). No late homework submissions will be accepted. A late or missed HW will receive a 0 score. Homework should be submitted in a "professional" form which allows a grader to read your solutions without unnecessary effort or ambiguity. In particular, your solution should either be typed or handwritten in a neat and legible form; if you submit scanned pages, they should be perfectly legible; submitted pages should be ordered with clear indication of which problem is being solved; if your homework solution consists of more than one page, pages must be stapled. Collected homework that does not satisfy these guidelines might receive up to a 50% penalty in the score. The homework assignments will count 30% towards the final grade.

HOMEWORK PROBLEMS:

(the list below will be updated during the semester)

Homework 1 - DUE  WED Jan 23 - Solution.
Homework 2 - DUE FRI Feb 1 - Solution.
Homework 3 - DUE MON Feb 18 - Solution.
Homework 4 - DUE Mon Feb 25 - Solution.
Homework 5 - DUE MON Mar 4 - Solution.
Homework 6 - DUE WED Mar 20 - Solution.
HW7: from p.215: 8; from p.224: 3; from p.225: 12,13,14; from p.231: 6,7 - see book extract - DUE DUE WED Apr 3 - Solution.
HW8: from p.232: 15; from p.239:4(b),5,6,10; from p.240: 15 - see book extract - DUE MON Apr 15 - Solution.
HW9: from p.260: 6; from p.261:11; from p.269: 5(a,b,f); from p.270: 8(a) - see book extract - DUE FRI Apr 26 - Solution.

There will be three tests in class counting 40% towards the final grade (tentatively, on Mon Feb 11, Fri March 22, Wed Apr 17 ). The worst of your 3 tests, will be half-dropped; that is, the 3 tests counts 40% towards the final grade, where the best two tests will count 16% each, the worst one will count 8%.
The final exam counts 30% towards the final grade. This is scheduled on FRI, MAY 3, 11-2.
Makeup tests will be allowed for justified and unavoidable absences (e.g., a car accident, a medical or family emergency). In this situation, you need to inform me as soon as possible to arrange for a make up quiz. If you know that you will miss a test/quiz, you need to contact me in advance. All arrangements for make-ups must be made via email. If you miss a test or quiz without justification, you will get a zero score.

Tests with solutions (to be updated during semester):

Test 1 ,   Test 2 ,   Test 3 .

 

The grade will be determined according to a set point scale: 90%-100%: A, 80%-89%: B, 70%-79%: C, 60-69% D; F is less than 60% (+ and - will also be used).