Math 265: Transition to Advanced Math
I am not teaching Math 265 this semester, but it is scheduled to run again in Fall 2016.
Old Math 265 Syllabi:
Meeting Information
Instructor: Lauren Williams
Meeting Times: MWF 9:1510:20 AM
Meeting Location: Hirt M209
Office: Old Main 404 (Tower)
Office Hours: Mon 10:4512 and 45, Tues 9:1512, Wed 10:4512, Fri 10:4512 and by appointment
Course Objectives
This course is designed to facilitate the mathematics studentâ€™s transition to courses requiring a higher level of mathematical maturity. Emphasis will be on the reading and writing of proofs, and on communicating mathematicallyâ€”both orally and in writing. Topics will include logic, set theory, functions, relations, and number theory.
In this course, you will:
 learn to write using formal, mathematical language with correct notation.
 learn to construct direct proofs, proof by contradiction, and proofs by induction.
 learn to read mathematics critically, and be able to determine whether a proof is sound or flawed.
 define relations between sets of objects and the properties of those relations.
 learn the basic definitions and principles of logic, set theory, combinatorics, and number theory.
 be exposed to several different areas of mathematics, via direct study or within examples designed to clarify other topics.
 learn to apply new techniques of problem solving to challenging material, both in this course and in future study.
Textbook
We will be using the book
A Gentle Introduction to the Art of Mathematics, Version 3.1SN, by Joe Fields. You will not need any additional materials for the course.
The author of this book has generously made it
available as a free pdf. You can also order a
printed copy from CreateSpace for $16 if you prefer, but this is not required for the course.
There is also a
workbook to accompany the text if you're looking for extra practice.
Homework
You will have homework assignments due approximately every week. These assignments will feature several questions taken from the text as well as other sources. Using proper mathematical notation and language will be a major part of your grade, aside from simply answering questions correctly. You will also be given additional suggested problems that will not be collected, but will help give you sufficient practice to succeed in the course. You are permitted and encouraged to work together on all assignments. Your lowest homework grade will be dropped when calculating your grade.
Homework assignments will be posted here, as well as distributed in class. Solutions will be posted shortly after assignments have been collected.
Due Date 
Assignment 
Solutions 
September 5 


September 10 


September 17 


September 24 


October 1 


October 15 


October 22 


October 29 


November 5 


November 19 


December 3 


Exams
We will have two in class exams on the following dates. You will be given an exact list of topics, along with a review sheet posted
here, approximately one week before each exam. Use of notes, textbooks, calculators, electronic devices, or other materials will not be permitted during an exam.
Your lowest exam grade will be replaced by your final exam grade, if your final exam grade is better. There are no make up exams; a missed exam grade will be replaced by your final exam grade. A second missed exam will receive a grade of 0, so please check your schedules carefully and ensure that you can attend all exams.
 Monday, October 6
 Monday, November 10
Exam review sheets will be posted here approximately one week before each exam:

Review Sheet 
Solutions 
Exam I 
Coming Soon (will be posted by September 29) 
Coming Soon (will be posted by October 4) 
Exam II 
Coming Soon (will be posted by November 3) 
Coming Soon (will be posted by November 8) 
Final Exam
The final exam will be cumulative, and is scheduled for Friday, December 12, 8:30  10:30.
Final Grades
Your final grade will be calculated as follows:
 30%  Average of 2 in class exams
 50%  Average of homework assignments
 20%  Final exam
Grading scale:
F 
D 
D+ 
C 
C+ 
B 
B+ 
A 
059 
6064 
6569 
7077 
7883 
8489 
9093 
94100 
Quiz and exam grades will be posted on Blackboard, so you can keep track of your progress at any time.
Other Course Information
 You are neither expected nor required to purchase any materials for the course aside from the required textbook. Graphing calculators and mathematical software could be used to check your work, but should not be relied on to do the work for you.
 I will attempt to return emails as thoroughly and promptly as possible. However, it is generally better to ask complicated questions during class or in office hours. If you have a question about the homework, it is quite likely someone else has the same question, so you're doing the class a favor by asking!
 I do not keep detailed lecture notes. It is highly recommended that you establish contacts among your classmates to get notes in case you miss class.
 Attendance is not required, but coming to class regularly will generally improve your grade. You are responsible for any work material covered in your absence. Please contact me if you are absent for an extended period.
Mathematics Department Student Learning Outcomes
Your written homework in this course will be used to assess your ability to effectively write mathematics. This assessment does not affect your grade, and a separate rubric will be used for the assessment vs your assignment grade.
Learning Differences
In keeping with college policy, any student with a disability who needs academic accommodations must call Learning Differences Program secretary at 8243017, to arrange a confidential appointment with the director of the Learning Differences Program during the first week of classes.
Support of the Mercy Mission
This course supports the mission of Mercyhurst University by creating students who are intellectually creative. Students will foster this creativity by: applying critical thinking and qualitative reasoning techniques to new disciplines; developing, analyzing, and synthesizing scientific ideas; and engaging in innovative problem solving strategies.
Extra Resources
Cut the Knot's Proof Page
A nice list of some simple but famous proofs, along with some fallacies.
Wolfram Alpha
If you're not already familiar with it, Wolfram's (free!) online math software is a great reference. Aside from performing calculations and drawing graphs, you can ask Alpha to provide definitions, explanations, and examples of many of the topics we'll see in class.
Sage
An open source mathematics software system. Runs natively on Linux and Mac, but you can also run it within your browser. Plenty of documentation to help offset the learning curve. Based on Python with plenty of useful packages, and you can contribute!
Course Schedule
The schedule below is approximate  topics covered on a particular day are subject to change. Exams and quizzes will take place as scheduled, with adjustments to material covered made when necessary. Any changes to material covered on quizzes will be announced in class and updated here.
Aug 27 
Class Introduction, Types of numbers

Aug 29 
Basic Number Theory, Relations

 
Sep 1 
No Class (Labor Day)

Sep 3 
Section 2.1 Predicates and Logical Connectives
Homework 1 Due

Sep 5 
Section 2.2 Implication

 
Sep 8 
Section 2.3 Logical Equivalences

Sep 10 
Section 2.4 Two Column Proofs
Homework 2 Due

Sep 12 
Section 2.5 Quantified Statements

 
Sep 15 
Section 2.6 Deductive Reasoning and Argument Forms

Sep 17 
Section 2.7 Validity of Arguments and Common Errors
Homework 3 Due

Sep 19 
Section 3.1 Direct Proofs of Universal Statements

 
Sep 22 
Section 3.2 More Direct Proofs

Sep 24 
Section 3.3 Contradiction and Contraposition
Homework 4 Due

Sep 26 
Section 3.4 Disproofs

 
Sep 29 
Section 3.5 By Cases and By Exhaustion

Oct 1 
Section 3.6 Existential Statements
Homework 5 Due

Oct 3 
Review for Exam I

 
Oct 6 
Exam I

Oct 8 
Section 4.1 Basic Notions of Set Theory

Oct 10 
No Class (Mid Semester Break)

 
Oct 13 
Section 4.2 Containment

Oct 15 
Section 4.3 Set Operations
Homework 6 Due

Oct 17 
Section 4.4 Venn Diagrams

 
Oct 20 
Section 5.1 The Principal of Mathematical Induction

Oct 22 
Section 5.2 Formulas for Sums and Products
Homework 7 Due

Oct 24 
Section 5.3 Other Proofs Using PMI

 
Oct 27 
Section 6.1 Relations

Oct 29 
Section 6.2 Properties of Relations
Homework 8 Due

Oct 31 
Section 6.3 Equivalence Relations

 
Nov 3 
Section 6.4 Ordering Relations

Nov 5 
Section 6.5 Functions Section 6.6 Special Functions
Homework 9 Due

Nov 7 
Review for Exam II

 
Nov 10 
Exam II

Nov 12 
Section 7.1 Counting

Nov 14 
Section 7.2 Parity and Counting Arguments

 
Nov 17 
Section 7.3 The Pigeonhole Principle Section 7.4 The Algebra of Combinations

Nov 19 
Section 8.1 Equivalent Sets
Homework 10 Due

Nov 21 
Section 8.2 Examples of Set Equivalence

 
Nov 2428 
No Class (Thanksgiving Break)

 
Dec 1 
Section 8.3 Cantor's Theorem

Dec 3 
Selected Topics
Homework 11 Due

Dec 5 
Review for Final Exam

 
Dec 12 
Final Exam 8:30  10:30
