University of Connecticut College of Liberal Arts and Sciences
Department of Mathematics
Tom Roby's Math 213 Home Page (Fall'07) "Transition to Advanced Math"

Questions or Comments?

Class Information

COORDINATES: Classes meet Tues/Thur. 11:00--12:15 in MSB 219. The registrar calls this Sec 001, #8522

PREREQUISITES: Some calculus, but we won't use it very much. More important is the ability to work hard on unfamiliar problems. This course itself is a prerequisite for most upper division courses in math.

TEXT: John D'Angelo & Doug West: Mathematical Thinking: Problem-Solving and Proofs, Prentice Hall 2000. Second edition 412+xx pages, 930 exercises, 180 figures ISBN 0-13-014421-6.

WEB RESOURCES: The homepage for this course is It will include a copy of the syllabus and list of homework assignments. I will keep this updated throughout the quarter.

GRADING: Your grade will be based on a midterm exam, a final exam, homework, and quizzes.

The breakdown of points is:

Midterm Final Quizzes Homework/Participation
25% 40% 15% 20%

EXAMS: The exam dates are already scheduled, so please mark your calendars now. No makeups will be given; instead if you have an approved reason for missing an exam, the final will count for the appropriately higher percentage. If you know you have a conflict, please let me know asap.

CONTENT: This content of this course is how to DO mathematics. The specific choice of topics is less important than your ability to come to grips with different kinds of mathematical thinking and writing. We plan to cover most of Chapters 1-8 and 13-14 of the text.

  • Numbers, Sets, and Functions
  • Language and Proofs
  • Induction
  • Bijections and Cardinality
  • Combinatorial Reasoning
  • Divisibility
  • Modular Arithmetic
  • The Rational Numbers
  • The Real Numbers
  • Sequences & Series

LEARNING GOALS: By the end of the course you should be able to

  • Explore unfamiliar mathematical problems using examples
  • Formulate precise mathematical statements ("conjectures") that can be proven or disproven.
  • Understand how to negate a mathematical statement and how to disprove a conjecture using a counterexample
  • Use various methods of proof, including mathematical induction, bijections, contradiction, and some epsilonics, to demonstrate the truth of mathematical facts.
  • Be able to communicate mathematics clearly orally and in writing
  • Discriminate between correct proofs, informal reasoning, wishful thinking, and falsehoods.

LEARNING: The only way to learn mathematics is by doing it! Complete each assignment to the best of your ability, and get help when you are confused. Come to class prepared with questions. Don't hesitate to seek help from other students. Sometimes the point of view of someone who has just figured something out can be the most helpful.

We will often spend classtime doing things in groups, presenting mathematics to one another, or having interactive discussions. There will not be time for "cover" all material in a lecture format so you will need to read and learn some topics from the book.

DISABILITIES If you have a documented disability and wish to discuss academic accommodations, or if you would need assistance in the event of an emergency, please contact me as soon as possible.

HOMEWORK: Homework will be assigned weekly I will collect homework and grade a pseudorandom sample of it.

You may find some homework problems to be challenging, leading you to spend lots of time working on them and sometimes get frustrated. This is natural. I encourage you to work with other people in person or electronically. It's OK to get significant help from any resource, but in the end, please write your own solution in your own words. Copying someone else's work without credit is plagiarism and will be dealt with according to university policy. It also is a poor learning strategy.

Date Sections Topics DUE
8/28 T Ch. 1 Quad. Formula, Inequalities, Sets Handout
8/30 R Ch. 1 Functions
9/4 T Ch. 2 Quiz #1
9/6 R Ch. 2 HW1 due: Ch. 1: #11,20,21,25,27,46,50
9/11 T Ch. 0 Building Evacuation (No Class) :-(
9/13 R Ch. 2 Quantifiers, Truth tables HW2 due: Ch.2: #10, 22, 26, 29, 36, 45,48, 51b
9/18 T Ch. 2 Contradiction, sqrt(2) irrational Quiz #2
9/20 R Ch. 3 Induction (triangle numbers)
9/25 T Ch. 3 Induction, Inequal 3.19, HW1 issues Quiz 3
9/27 R Ch. 3 Strong Induction HW3:Ch. 3:#16,18,23,28,37,39,49ab,57,62
Now due 10/2
10/2 T Ch. 4 Bijections Quiz #3 Rewrite, Quiz #4
10/4 R Ch. 4 Cardinality HW4: #1,2,5,7,11,12,21,25cd,27
10/9 T Ch. 1-5 Catchup Day, Combinations Quiz #4
10/11 R Ch. 1-4 Review Day Practice Midterm
10/18 R Ch. 5 Permutations
10/23 T Ch. 5 Combinations & Identities
10/25 R Ch. 6 Divisibility HW5: Ch.5: #10,11,12,30,39,49,52,58
10/30 T Ch. 6 Divisibility Quiz #5 (Ch. 6(-) probs.)
11/1 R Ch. 7 Modular Arithmetic HW6: Ch.6: #8b,9cd,18,23,24,28,30,34,37,39
11/6 T Ch. 7 Modular Arithmetic Midterm Rewrites due
11/8 R Ch. 8 Rational Numbers HW7: Ch7: #6,13,15,17b,21,24,34,35,43
11/13 T Ch. 13 Real Numbers
11/15 R Ch. 13 Real Numbers HW8: ch5:13,42,57; ch6:40; ch7:19,23,31; ch8:1,12
11/27 T Ch. 13-14 Sequences & Limits HW8 due; Quiz #7 (Ch. 13(-) probs.)
11/29 R Ch. 14 Series HW9: Ch13: 8,10,16,22,25,27,30,34
12/4 T Ch. 14 Series Quiz #8 (Ch. 14(-) probs.)
12/6 R All chapters Review Day Practice Final
12/7 F Midterm & Rewrites Review Session MEET AT 3:00pm in ROOM TBA (Meet in MSB 219 else)

Interesting Links

  • Maybe I'll add some later.


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