Math 34001: Fundamental Concepts of Algebra
Spring 2015
Course Information
- Office Hours
- Syllabus
- Textbooks:
- Our Main Textbook (last modified: Wed, 22 Apr 2015, 12:48 pm) We will build this together through the course of the semester!
- You will be assigned reflective essays based on readings from The Mathematical Experience by Philip J. Davis and Reuben Hersh.
Other Useful and Interesting Links
- Flashline
- The Five Big Lies About Campus Rape, Claire Potter, The Chronicle of Higher Education, August 13, 2013
- The Pursuit of Beauty, the story of Yitang Zhang and the prime gaps problem.
I will expect you to read mail sent to your @kent.edu account regularly. I will occasionally send the class emails via Flashline.
New course for Fall 2015: The Mathematics of Social Choice
Semester Schedule with Homework Assignments |
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Date | Prepare for Class Reading Sign-up Homework Presentations |
Hand-in Homework | Reflective Essays | Announcements | ||
Week 1 | Monday, 1/12/15 | X | X | X | Snow Day: No Class | |
Wednesday, 1/14/15 | X | X | X | |||
Friday, 1/16/15 | 4-10 | X | X | |||
Week 2 | Monday, 1/19/15 | X | X | X | MLK Day: No classes | |
Wednesday, 1/21/15 | 11-18 | Proposition 9 | Essay 1 | |||
Friday, 1/23/15 | 19-28 | X | X | Quiz 1 covers 1-18.
Be prepared to state definitions, complete the statements of propositions,
identify algebraic properties of various sets and operations.
On future quizzes, you will be asked to prove propositions, but not on this first quiz.
Quiz 1 solution |
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Week 3 | Monday, 1/26/15 | 19-28 | HW1: Rewrite and resubmit proof of Proposition 9,
based on class discussion and comments on your first attempt.
This would be a good time to read some of the suggestions for writing proofs posted below.
HW1 student solution |
X | ||
Wednesday, 1/28/15 | 29-35 | X | Essay 2 | |||
Friday, 1/30/15 | 29-35 | X | X | Quiz 2 will cover 1-28.
Be prepared to state definitions, complete the statements of propositions,
identify algebraic properties of various sets and operations, and to prove propositions.
Quiz 2 solution |
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Week 4 | Monday, 2/2/15 | X | X | X | Snow Day: No classes | |
Wednesday, 2/4/15 | X | HW2: Carefully write up proofs of
Prop. 27, Prop. 29, and Cor. 30.
(Item 30 has been fixed on the sheet.)
Your work can and should be informed by the discussions in your small groups and in class, but your write-up should be your own work, in your own words. If you haven't already done so, please read the proof-writing guidelines below. HW2 solution |
Essay 3
A nice example and another nice example |
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Friday, 2/6/15 | 36-44 | X | X | Quiz 3 will cover 1-35.
Quiz 3 solution |
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Week 5 | Monday, 2/9/15 | X | HW3: Carefully write up proofs of Propositions 38, 39, 41, and 43. | X | ||
Wednesday, 2/11/15 | 1-54 | X | Essay 4 | |||
Friday, 2/13/15 | 1-55 | X | X | Quiz 4
and Quiz 4 solution |
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Week 6 | Monday, 2/16/15 | 1-55 | X | X | ||
Wednesday, 2/18/15 | 1-55 | HW4: Carefully write up proofs of Propositions 38, 41, 48, and 49 | X | Quiz 5
and Quiz 5 solution |
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Friday, 2/20/15 | Snow Day: No classes. | |||||
Week 7 | Monday, 2/23/15 | X | X | X | ||
Wednesday, 2/25/15 | X | X | X | |||
Friday, 2/27/15 | X | X | X | Exam 1
Exam 1 solution |
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Week 8 | Monday, 3/2/15 | X | X | X | ||
Wednesday, 3/4/15 | 59-66 | X | X | |||
Friday, 3/6/15 | 59-75 | X | X | |||
Week 9 | Monday, 3/9/15 | 59-75 | Essay 5 (self assessment) | Quiz 6
and Quiz 6 solution |
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Wednesday, 3/11/15 | HW5: Write up careful proofs of
Prop. 66(i),
Prop. 66(v), Prop. 69, Prop. 71, and Prop. 75.
HW5 solution |
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Friday, 3/13/15 | 70-83 | Quiz 7
and Quiz 7 solution |
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Week 10 | Monday, 3/16/15 | X | X | X | Class canceled due to instructor illness. | |
Wednesday, 3/18/15 | X | X | X | Class canceled due to instructor illness. | ||
Friday, 3/20/15 | 70-83 | X | X | |||
Have a Great Spring Break! | ||||||
Week 11 | Monday, 3/31015 | 84-87 and 96-104 | X | X | ||
Wednesday, 4/1/15 | 88-95 | X | X | |||
Friday, 4/3/15 | X | X | X | Quiz 8
and Quiz 8 solution |
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Week 12 | Monday, 4/6/15 | 105-108 | HW6: Write up Prop 88, Lemmas 90, 91, 92,
and Explorations 105(c), 106(c), 107(c), and 108(c).
HW6 solution |
X | ||
Wednesday, 4/8/15 | X | X | X | |||
Friday, 4/10/15 | X | X | X | Exam 2
Exam 2 solution |
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Week 13 | Monday, 4/13/15 | X | X | X | ||
Wednesday, 4/14/15 | 114-121 | X | X | |||
Friday, 4/17/15 | 122-134. (Can you make a better conjecture?) | X | X | Quiz 9 covers 114-125
Know the definition of "divides" and how to prove Conjecture 122. For the other conjectures, on the quiz, you need only know whether
they're true or false.
Quiz 9 solution |
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Week 14 | Monday, 4/20/15 | 122-134 | HW 7 : Write up 123, 124, 125, 131, 132. | X | ||
Wednesday, 4/22/15 | 135-151
You are not responsible for proofs of 139, 140, 143, 144 (statements only). |
X | X | |||
Friday, 4/24/15 | 145-159 | X | X | Quiz 10 covers 145-155 .
Quiz 10 solution |
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Week 15 | Monday, 4/27/15 | X | X | |||
Wednesday, 4/29/15 | 158, 159, 171, 172, 173 | X | X | |||
Friday, 5/1/15 | X | X | X | |||
Finals Week | Tuesday 5/5/15 10:15--12:30 | Essay 6
Here's your chance to brag to me about the progress you've made this semester! |
Final Exam covers 1-177, with an emphasis on the Chapter on Number Theory | |||
Last updated Fri, 01 May 2015, 12:12 pm |
Guidelines for Writing Mathematics
- Ten Tips for Writing Mathematical Proofs by Katharine Ott.
- Some Remarks on Writing Proofs by John M. Lee.
- Guidelines for writing proofs (from Mathematical Reasoning: Writing and Proof by Ted Sundstrom).
- Some mathematical terminology (from Mathematical Reasoning: Writing and Proof by Ted Sundstrom).
- Mathematics and proofs (from A First Course in Abstract Algebra by John B. Fraleigh).
- Mathematical reasoning (from An Introduction to Abstract Mathematics by Bond and Keane).