Math 261 Bard College

Proofs & Fundamentals

Course:  Math 261, Spring 2013

Time & Place:  TR 3:10pm–4:30pm in Olin LC 115

Instructor:  Maria Belk (mbelk@bard.edu)

Office Hours:


Dedicated Tutors:

Tutor Office Hours:  TBA

Math Study Room:  Sunday through Thursday, 710 pm in RKC 111

Announcements

Takehome Final: The takehome final is due on Tuesday, May 21. You must work completely on your own, consulting only the textbook, your course notes, and your homeworks as references. If you have questions, you can come to my office hours or ask me via e-mail. Good luck!

Number Theory Notes: Our next topic in class is some elementary number theory. This topic is not in the textbook, so here are some notes on the topic:

Reading Assignment: Read the Number Theory Notes.

Homework 10: The tenth homework assignment is due on Friday, May 10. Your solutions should be written in LaTeX.

In-class Final: The in-class portion of the final exam will be on Thursday, May 2. Here are practice problems and solutions:

Homework 9: The ninth homework assignment is due on Friday, April 26. Your solutions should be written in LaTeX.

Project Information

Part of the requirements for this class include a final project. Here is some basic information about the project:

Project Topics

There are two basic options for your project: In the following list of topics, research topics are marked with an R, and book topics are marked with a B. Some topics might work either way, so these are marked RB. These topics are only suggestions—you should feel free to invent your own topic, or discuss other possibilities with me:

Project Timeline

Here is a timeline of due dates for the project:

LaTeX

You are required to write homework solutions in LaTeX. Here are some links to get you started:

If you want to download LaTeX to your own computer, Ethan recommends TeXShop for Mac users, and proTeXt for PC users:

Sample Assignments

Two sample assignments in LaTeX:

Homework Solutions

Here are solutions to the homeworks:

Takehome Midterm: The takehome portion of the midterm was due on Friday, March 22. Here is the midterm and solutions:

Midterm: The in-class portion of the midterm exam was on Thursday, March 14. Here are practice problems and answers:

Schedule

WeekDates Practice Problems Homework
Week 1 Jan. 29, 31 None None
Week 2 Feb. 5, 7
  • 1.2 # 1, 5, 7, 8, 12, 13
  • 1.3 # 8, 9
  • 1.4 # 2
  • 1.4 # 1 (parts 3–6)
Week 3 Feb. 12, 14
  • 1.5 # 1, 2, 6
  • 2.2 # 2, 3, 4, 5
  • 1.5 # 11 (part 3)
  • In paragraph form:  1.4 # 1 (parts 4 and 6)
  • In both two column and paragraph form:  2.2 # 6, 7
Week 4 Feb. 19, 21
  • 2.4 # 2, 4, 7
  • 1.5 # 8
  • 2.3 # 3, 5
  • 2.4 # 3, 8
Week 5 Feb. 26, 28
  • 2.5 # 3, 5, 7
  • 3.2 # 2, 3, 4, 7, 8
  • 2.3 # 7
  • 2.5 # 4, 6, 8
Week 6 March 5, 7
  • 3.3 # 1, 3, 4, 13
  • 3.4 # 1, 2
  • 3.2 # 14
  • 3.3 # 5, 18, 19
Week 7 March 12, 14    
Week 8 March 19, 21   Takehome Midterm (TeX, PDF)
Spring Break      
Week 9 April 2, 4
  • 4.1 # 1, 2, 3
  • 4.2 # 1, 3
  • 4.3 # 1
  • 4.4 # 1, 2
  • 4.3 # 3, 5, 9
Week 10 April 9, 11  
  • 4.4 # 4, 11, 14
Week 11 April 16, 18
  • 5.1 # 3
  • 5.2 # 1
  • 5.2 # 4, 5, 6, 8
Week 12 April 23, 25
  • 5.3 # 1, 2, 3, 8, 9
  • 5.3 # 4 (part 1) and # 6
  • 6.3 # 1 (parts 1, 2, and 5)
Week 13 May 2    
Week 14 May 7, 9  
Week 15 May 14, 16    
Week 16 May 21    

Course Policies

Introduction

This course is an introduction to the language and methodology of modern mathematics. Topics covered include an introduction to mathematical logic, axiomatic systems, sets, relations and functions, cardinality, and mathematical structures. In addition, you will be learning how to communicate using the precise language of mathematicians, including the writing of formal proofs. This material is fundamental to any serious study of mathematics beyond the level of calculus.

Prerequisites

The prerequisite is Math 142 (Calculus II) or permission of the instructor. We will not actually be using much calculus, but the course will require the sort of mathematical maturity and familiarity with abstract reasoning that tends to be developed in a calculus class. It would also be helpful to have taken another 200-level math course beforehand such as Math 213 Linear Algebra with Ordinary Differential Equations.

Textbook

The textbook is Proofs and Fundamentals, A First Course in Abstract Mathematics, by our own Ethan Bloch. We plan to cover most of chapters 16, with selected other topics as time permits.

Homework

There will be weekly homework assignments, which will often involve the writing of formal proofs. You are encouraged to work together on the homework, but you should write up your own solutions individually, and you must acknowledge any collaborators.

Writing Your Solutions

A major goal in this course is to learn to write formal mathematical proofs. A good proof often requires multiple drafts to get right, and you will need to get into the habit of editing your homework solutions after you write them.

Because it makes editing easier, and because it is the universal standard for mathematical writing, all of your homework solutions must be written in LaTeX. If you haven't used LaTeX before, I recommend starting with Ethan Bloch's LaTeX web page for Bard students, which has links to many helpful resources.

Exams, Project, and Grading

In addition to the weekly homework assignments, much of your grade will be based on a midterm exam and final exam. Both exams will have an in-class part and a takehome part. There will also be a project due near the end of the semester, which will consist of an in-class presentation and a short write-up. These items will be weighted as follows:

Homework 40%
Midterm 20%
Final 20%
Project 20%

Feedback

Do you have any suggestions for the class? Let me know by using the following feedback form!
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