MATH 310 Introduction to Analysis

Fall 2004, Section 0201, Prof. Raymond Johnson

Exam Schedule
First Exam:
Wednesday, 29 September
Second Exam:
Wednesday, 27 October
Third Exam:
Wednesday, 8 December
Final Exam:
Tuesday, 14 December 2004, 1:30 - 3:30.

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, Wednesday, and Friday, 1:00-1:50
Math Building 0303.

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, 13-16 of D'Angelo-West.

Math 310: Provisional Schedule

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

WEEKMondayWednesdayFriday
Aug 30-Sep 3 11-22(Q1)
Sep 6 - Sep 10Labor Day Holiday23: Induction
Sep 13-Sep 17 3:Induction 3:Induction4:Numbers(Q2)
Sep 20-Sep 24 4:Mappings 4: Mappings8:Rational Numbers
Sep 27-Oct 1 Review EXAM #112: Recurrences
Oct 4- Oct 8 13:Real Number 13: Sequences13:Counting (Q3)
Oct 11-Oct 15 14:Sequences 14: Sequences14:Sequences (Q4)
Oct 18-Oct 22 14:Sequences 14: Cauchy Sequences14:Sequences (Q5)
Oct 25-Oct 29 Review EXAM #214:Series (Q4)
Nov 1-Nov 5 14: Comparison Tests 14:Geometric Series Make Up Quiz
Nov 8- Nov 12 14: Cauchy condensation 14:Series14:Telescoping Series
Nov 15- Nov 19 14: Alternating Series 14: Ratio and Root Tests 15: Continuity
Nov 22- Nov 26 15: Continuity 15: Continuity & Discontinuity Holiday
Nov 29- Dec 3 15: Continuity 15: Continuity Class cancelled
Dec 6- Dec 10 16: Differentiability EXAM #3 Review

Homework Problems