# MATH 215 Introduction to Advanced Mathematics

## Fall 2013

Instructor: David Marker
TA: Phillip Wesolek, office Hours M 4:30-5:30 W 5-6 in Math Learning Center 430 SEO
Call Number: 24546
Class Meets: 10:00 MWF 313 Taft Hall
Office: 411 SEO
Office Hours: T 1:30-2:30, W: 11:00-12:30
phone: (312) 996-3069
e-mail: marker@math.uic.edu
course webpage: http://www.math.uic.edu/~marker/math215-F13

### 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, infinite sets and elementary number theory. As time permits, we will cover much of Parts I-IV and part of Part V of the text.
A detailed week-by-week syllabus will be posted at
http://www.math.uic.edu/~marker/math215-F13 /wtw.html

### Practice Problems and Problem Sets

Doing problems is the way to learn mathematics!

Each chapter of the text has a number of exercises. 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 grammatical sentences. Since learning to write proofs is the central goal of the course, you will be graded on the clarity of your writing.

All handouts and assignments are posted on the public course webpage. Solutions to problem sets and midterms will be posted on the course page on Blackboard.

You may discuss homework problems with other students, but you must write up your solution independently.

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.
This course is prerequisite for all advanced theoretical courses in the department, particularly Math 313, 320 and 330. To receive a grade of C or better you must master the material in the course and be able to write proofs at a level where you are likely to be able to pass these more advanced courses.

Midterm 1: Friday October 4
Midterm 2: Friday November 15
Final Exam: Friday December 13 10:30-12:30

### 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 15 15.2, 15.3, 15.4, 15.5
• Chapter 16 16.1, 16.2
• Chapter 17 17.1, 17.2, 17.3
• Chapter 18 18.1, 18.2, 18.3
• Chapter 22: 22.1