MATH 215
Introduction to Advanced Mathematics
Fall 2006
For Fall 2012 Section click here
Instructor: David Marker
Call Number: 24546
Class Meets: 11:00 MWF 208 Taft Hall
Office: 411 SEO
Office Hours: M,W,F 1010:50, W 122
phone: (312) 9963069
email: marker@math.uic.edu
course webpage: http://www.math.uic.edu/~marker/math215
Text
 P. Eccles, An Introduction to Mathematical Reasoning, Cambridge University Press.
Prerequisites
Grade of C or better in MATH 181 and approval of the department. Description
This is a first course is a first course in theoretical mathematics. It is a prerequisite to all advanced theoretical courses in the department.
The Primary Goal of the course is to learn how to create and write mathematical proofs. We will introduce basic proof techniques, like proofs by induction and contradiction. We will also learn some basic mathematics that will be used in many advanced courses including: sets, functions, equivalence relations, cardinality and infinite sets. As time permits, we will cover most of Parts IIII and parts of Part V of the text.
A detailed weekbyweek syllabus will be posted at
http://www.math.uic.edu/~marker/math215/wtw.html Practice Problems and Problem Sets
Doing problems is the way to learn mathematics!
Each chapter of the text has a number of excercises. These exercises have solutions in the back of the book. Below I will pick out several of these from each chapter and encourage you to try them and check your answers in the back of the book. You are welcome to come talk to me about these problems.
There will be weekly problem sets that will be collected and graded. The two lowest grades will be dropped. Late homework will be accepted only in exceptional circumstances.
Most problem sets will consist of writing proofs. All proofs must be written in complete gramatical sentences. Since learning to write proofs is the central goal of the course you will be graded on the clarity of your writing.
You may discuss homework problems with other students, but you must write up your solution independently. Grading
There will be 2 midterm exams and a final exam. Each midterm will count for 25% of your final grade. The final will count for 35% and the problem sets will count for 15%. The lowest two problem set grades will be dropped.
Midterm 1: Friday October 6
Midterm 2: Friday November 17
Final Exam: Thursday December 14, 8:0010:00am
Problem Sets
 Problem Set 1: (Due Friday September 8) [ REVISED 9/3]
 Problem Set 2: (Due Friday September 15)
 Problem Set 3: (Due Friday September 22)
 Problem Set 4: (Due Friday September 29) pg 55: 14, 16, 17, 18
 Problem Set 5 (Due Friday October 13)
 Problem Set 6: (Due Friday October 20) pg 115117: 4, 7, 11, 12
[on problem 11, for each part decide if the statement is TRUE or FALSE and
justify your answer by giving a proof or a counterexample.]
 Problem Set 7 (Due Monday October 30)
Note: due date revised
 Problem Set 8: (Due Friday November 3) pg 118: 16 i).ii), iii),
vi), 18, 19
 Problem Set 9: (Due Friday November 10) pg 118119: 20 i), iii),
21, pg 182: 1
5 point bonus: pg 182: 2
 Problem Set 10 (Due Wednesday November 22)
 Problem Set 11 (Due Friday December 1)
 Problem Set 12 (Due Friday December 8)
Practice Problems
 Chapter 1: 1.2, 1.4, 1.5

Chapter 2: 2.1, 2.3, 2.5
 Chapter 3: 3.1ii), 3.5, 3.6
 Chapter 4: 4.1, 4.3, 4.4, 4.6
 Chapter 5: 5.2, 5.4, 5.5, 5.6
 Chapter 6: 6.1, 6.4, 6.5, 6.6, 6.7
 Chapter 7: 7.2, 7.3, 7.4, 7.6, 7.8
 Chapter 8: 8.2, 8.3, 8.5
 Chapter 9: 9.1, 9.3, 9.4, 9.5, 9.7
 Chapter 10: 10.1, 10.3, 10.4
 Chapter 11: 11.1
 Chapter 12: 12.3, 12.4
 Chapter 14: 14.1, 14.2, 14.3, 14.4
 Chapter 22: 22.1
Handouts and Useful Links
David Marker's homepage
Last Updated 12/6/06