This syllabus is subject to change at the instructor's discretion.
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Syllabus of Math 220 (W - class), Section 970 (honors)

Foundations of Mathematics, Fall 2014

Instructor Peter Kuchment

Office Rm. Blocker 614A, Telephone (979)862-3257

E-mail:, Home Page: /~kuchment


The purpose of the course is to provide students with important foundational skills that will prepare them to be successful in higher level courses. The main thrust is to teach students how to understand, create, and communicate proofs. Some frequently used types of proofs will be introduced. Several mathematical topics from logic, set theory, etc. will be addressed, where the newly learned techniques can be applied.

This is a W (writing) course, which means that close attention will be paid to students' ability to write mathematical statements and proofs mathematically and grammatically correctly. About one third of the grade will depend on the writing.
The instructor will be providing examples and recommendations concerning math writing.
The following little book (not required) is a good source for many such recommendations:
Donald E. Knuth, Tracy Larrabee, Mathematical Writing, The Mathematical Association of America 1989. ISBN 978-0883850633.
Some other books of this kind:
Norman E. Steenrod,, Paul R. Halmos, et al, How to Write Mathematics, Amer. Math. Soc. 1973. ISBN-13: 978-0821800553. A collection of articles by famous mathematicians concerning writing.
Nicholas J. Higham, Handbook of Writing for the Mathematical Sciences, SIAM 1998. ISBN-13: 978-0898714203
Steven Krantz, A Primer of Mathematical Writing: Being a Disquisition on Having Your Ideas Recorded, Typeset, Published, Read & Appreciated

And here is the timeless treasure: a tiny beautiful book on writing:
William Strunk Jr., E. B. White, The Elements of Style, Longman 1999 (there are zillions of other editions). ISBN-10: 020530902X, ISBN-13: 978-0205309023.

Catalog description

Foundations of mathematics, including topics from logic, set theory, combinatorics, and number theory.


MATH 148, MATH 152 or MATH 172 or equivalent with a grade of C or better and eligibility for a honors class.

Tests, quizzes, and homework

  1. Weekly home assignments or quizzes - 20% of the grade.
  2. Two mid-term exams - 20% each.
  3. Term paper - 15%.
  4. Final exam - 25%

It is advised that besides doing homework, students try to solve other problems after the sections studied. In case of any difficulties contact the instructor.

Tentative schedule of the course


Chapters and sections

Home assignments (to be handed in BEFORE the class on the due date).
Notation Section 2.3 #2(a,c,e) means the parts a), c), and e) of the problem #2 after Section 2.3. If it says just #2, you need to solve the whole problem #2.

Tests, quizzes, term papers (dates are flexible and will be confirmed closer to a test).

1, Sept. 1 - 6

Sections 1.1 Statements, 1.2 Compound statements

Assignment #1 - Sect. 1.1 #1 (b,c,e,f,h,j,k); 2(b,c,e,f,h); 3(b,c,e,f,h); 5(b,c,e,f); 6; 7(b,c), D5, D6, D8. Section 1.2. #3, 5(b,c,e,f), 15a, 16, D1, D2, D4. Extra credit: Section 1.1. #8, D3 . Due September 11th.

2, Sept. 8 - 13

Section 1.3 Implications


3, Sept. 15 - 20

Section 1.4 Contrapositive and converse

Assignment #2. Section 1.3 #1b,c; 2c; 3b; 4, 5, 6, 8, 9, D2; Section 1.4 # 4a,b; 5, 16, 17, 20, 21, D1, D2, D4 . Due Tuesday September 23rd.

4, Sept. 22 - 27

Sections 2.1 - 2.3 Sets


5, Sept. 29 - Oct. 4

Sections 6.1, 6.2. Infinite sets


6-7, Oct. 6 - 21

Infinite sets


Exam 1, Oct. 9 on logic (1.1 - 1.4) and sets (2.1 - 2.3, 6.1, 6.2)

7, Oct. 13 - 18

Sections 5.2, 2.3 - Induction. Pigeonhole principle

Assignment #3. Section 2.3 #2, 4, 5 (b,c,e,f), 11, 14, 23; Section 5.2 # 1c, 3, 4b, 14; Section 6.1 #11 (a,b,c,d,e) Section 6.2 # 3, 4, 7 (b,c,e,f,h). Due Tuesday October 28th.

8 - 10, , Oct. 23 - Nov. 8

Sections 3.1 - 3.3. Functions. Sections 5.1 - 5.2 Elementary Number Theory


Oct. 28. Outline is due (15 points)

11, Nov. 10 - 15

Section 5.3

Assignment #4. Due N0vember 11th.

Nov. 11, Two copies of typed draft are due. (20 points)
Nov. 13, copies for editing are distributed

12 - 13, Nov. 17 - 22

Section 5.4


Nov. 18 - edited drafts are due (10 points)

Nov. 18 - Exam 2 on functions and number theory (3.1 - 3.3, 5.1 - 5.4)

14 - 14.5, Nov. 24 - Dec. 9



Nov. 24, HW Assignment #5 is due: Section 5.3 # 1,3,4(a),10(a,b),12,13. Extra Credit (no partial credit): D1, D2, D3 Dec 4. Term papers are due (45 points)

December 17, Wednesday, 8-10 a.m.

Additional office hours before the final exam: TBA

Comprehensive Final exam: December 17, Wednesday, 8-10 a.m.


Percentage of points


90% and higher


80% and higher


70% and higher


60% and higher


Less than 60%


Academic Calendar

Final Exams Schedule

Class Announcements, E-Mail Policy and Communications:

Class announcements will be posted on my homepage and emailed to your NEO accounts. It is your responsibility to check the accounts daily.
E-mail (kuchment AT is the preferred way to contact me.
When writing to me, please include your full name and "Math 220". Use your NEO e-mail account to send me e-mails.

Make-up policy:

Make-ups for missed quizzes, home assignments and exams will only be allowed for a university approved excuse in writing. Wherever possible, students should inform the instructor before an exam or quiz is missed. Consistent with University Student Rules , students are required to notify an instructor by the end of the next working day after missing an exam or quiz. If there are confirmed circumstances that do not allow this (a written confirmation is required), the student has two working days to notify the instructor. Otherwise, they forfeit their rights to a make-up.

Late work

Late work will not be accepted, unless there is an university approved excuse in writing. In the latter case student has a week to submit the work.

Grade complaints:

Sometimes the instructor might make a mistake grading your work. If you feel that this has happened, you have one week since the graded work was handed back to you to talk to the instructor. If a mistake is confirmed, the grade will be changed. No complaints after that deadline will be considered.

Students with Disabilities:

The Americans with Disabilities Act (ADA) is a federal anti-discrimination statute that provides comprehensive civil rights protection for persons with disabilities. Among other things, this legislation requires that all students with disabilities be guaranteed a learning environment that provides for reasonable accommodation of their disabilities. If you believe you have a disability requiring an accommodation, please contact Services for Students with Disabilities (Cain Hall, Room B118, or call 845-1637).

Copyright policy:

All printed materials disseminated in class or on the web are protected by Copyright laws. One xerox copy (or download from the web) is allowed for personal use. Multiple copies or sale of any of these materials is strictly prohibited.

Scholastic dishonesty:

Copying work done by others, either in class or out of class, looking on other student?s papers during exams or quizzes, having possession of unapproved information in your calculator/computer/phone, etc., and/or having someone else do your work for you are all acts of scholastic dishonesty. These acts, and other acts that can be classified as scholastic dishonesty, will be prosecuted to the full extent allowed by University policy. In this class, collaboration on graded assignments, either in class or out of class, is forbidden unless permission to do so is granted by the instructor. For more information on university policy regarding scholastic dishonesty, see University Student Rules at
"An Aggie does not lie, cheat, steal, or tolerate those who do." Visit and follow the rules of the Aggie Honor Code.


This syllabus is subject to change at the instructor's discretion

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Last revised November 7th, 2014