MATH 310 Introduction to Analysis

Summer 2008, Section 0101, Prof. Raymond Johnson

Office Hours

Exam Schedule

First Exam:: Wednesday, 11 June
Second Exam:: Wednesday, 25 June
Third Exam:: Wednesday, 9 July
Final Exam:: Friday, 11 July

Grading Policy

Grades will be based on three hour exams counting 100 points each, homework and quizzes worth 100 points, and a final examination that is worth 200 points.

Class Schedule

The class meets according to the following schedule:

Monday, Tuesday, Wednesday, Thursday, and Friday, 8:00-9:20: Math Building 0101.

Tutoring

Eric Hamilton is available for tutoring in Room 0403 from 12:30pm until 2:30pm from June 2 through July 11.

Topics

The immediate purpose of this course is to prepare students for Math 410. Its general goal is to develop the student's ability to construct a rigorous proof of a mathematical claim. As a side benefit, the student is made aware of various mathematical results that are of interest to those wishing to analyze a particular mathematical model. Math majors may not use this course for one of their upper level mathematics requirements.

PREREQUISITES Math 141 with Math 241 as a corequisite.
TOPICS: Some Logic; Direct proofs; Contrapositive proofs; Proofs by contradiction
Set Relations: Equivalence relations; Discussion of "modulo"
Cardinality: Size of sets; Countability; Bernstein's Theorem
Induction: First principal of finite mathematical induction; Second principal of finite mathematical induction; Applications
Recursive Equations: Problems expressible as a difference equation; Verification of solutions using induction
Pigeonhole Principle: Problems which can be solved by utilizing partitions
Completeness: Greatest lower bounds; Least upper bounds
Sequences: Convergence; Monotone convergence theorem; Bolzano-Weierstrass theorem; accumulation points; Contraction mapping principle

Student Conduct Code

The University of Maryland, College Park has a nationally recognized Code of Academic Integrity, administered by the Student Honor Council. This Code sets standards for academic integrity at Maryland for all undergraduate and graduate students. As a student you are responsible for upholding these standards for this course. It is very important for you to be aware of the consequences of cheating, fabrication, facilitation, and plagiarism. For more information on the Code of Academic Integrity or the Student Honor Council, please visit the Student Honors Council web site.

Topics in D'Angelo-West ISBN 0-13-014412-6

We wil cover parts of Chapters 1-4,8, 10, 13-14 of D'Angelo-West.

Math 310: Provisional Schedule

Chapters are from Mathematical Thinking: Problem-Solving and Proofs, 2nd edition by D'Angelo-West.

WEEK	Monday	Tuesday	Wednesday	Thursday	Friday
Jun 2-Jun 6	1	1-2	2(Q1)	2	3:Induction(Q2)
Jun 9 - Jun 13	3:Induction	4: Numbers & Review	EXAM #1	4:Mappings	4: Mappings (Q3)
Jun 16-Jun 20	4: Mappings & 7: Modulo	8: Rational Numbers	12: Recurences(Q4)	13: Real Numbers & Counting	13:Sequences(Q5)
Jun 23-Jun 27	13:Sequences	13:Sequences	EXAM #2	14: Sequences	14: Sequences (Q6)
June 30-Jul 4	14: Comparison Tests & Geometric Series	14: Comparison Tests & Geometric Series(Q7)	14: Cauchy condensation	14:Telescoping Series(Q8)	HOLIDAY
Jul 7-Jul 11	14: Ratio and Root Tests	14: Ratio and Root Tests(Q9)	EXAM #3	14: Contraction Mapping Principle(Q10)	FINAL EXAM

Homework Problems

Chapter 1 p. 20 Problems 9,13,17,18,20,32,42, 46, 49
Chapter 2 p. 44 Problems 4, 5, 10, 12, 15, 17, 18, 24,25,34,35, 36
Chapter 3 p. 72 Problems 8,15,16,17,21,26,27,30,31,35,41,43,50,56,57
Chapter 4 p. 95 Problems 5, 12, 13,20, 22,26,27,33,39,40,45
Chapter 7 p. 151 Problems 1, 2,3, 4, 5, 6, 10, 24
Chapter 8 p. 166 Problems 9, 11,21, 22,23,31
Chapter 12 p. 250 Problems 1,2, 3, 4, 5, 6, 12,19,31
Chapter 13 p. 268 Problems 8,11,12, 13,20, 22,23,25,26.29,30
Chapter 14 p. 287 Problems 15,16,18-21, 24-27
Chapter 14 p. 287 Problems 33,34,35,42-47, 53,56,58,59 (Series)
Chapter 15 p. 304 Problems 11, 13, 14-16.