MATH 49995 004, Introduction to Mathematical Thinking and Proofs, Spring 2007

MWF 9:55-10:45 AM, MSB 120
INSTRUCTOR: Sean Sather-Wagstaff
E-MAIL (replace " at " with "@"): sather at
PHONE: 672-9090
OFFICE HOURS: TR 10:00-11:50 AM, and by appointment
PREREQUISITES: MATH 12003 or 21001 or permission of instructor



REQUIRED TEXT: Mathematical Thinking: Problem-Solving and Proofs, Second Edition, by D'Angelo and West

COURSE DESCRIPTION: A course designed to aid students in the transition from lower division courses (calculus, linear algebra) to upper division courses. Introduces tools and topics useful in most upper division courses. Includes an introduction to logic and the language of proofs, proof techniques, problem-solving techniques, basic number theory, sets, functions, cardinality, rational numbers, real numbers, and complex numbers.

This will not be a traditional mathematics course. The instructor will not lecture during most class meetings. Instead, class time will be devoted to group discussion of the assigned reading and exercises and individual presentations of solutions to assigned exercises.

COURSE GRADES: Student grades are based on weekly homework assignments, attendance and participation, two (2) midterm examinations, and one (1) comprehensive final examination. Weights are summarized in the following table.

Homework: 20%
Attendance and participation: 25%
Midterms: 15% each
Final Exam: 25%

Final grades will be assigned according to the following percentages.

A 93-100% A- 90-92.9%
B+ 87-89.9% B 83-86.9% B- 80-82.9%
C+ 77-79.9% C 73-76.9% C- 70-72.9%
D+ 67--69.9% D 60-66.9%
F 0-59.9%

READING: I will make a reading assignment at the end of each class meeting. Reading assignments will also be listed below. Much of the next class meeting will be based on a discussion of the reading. Your participation score for that day will be based in part on your ability and willingness to discuss the reading in class, so you must keep up with the reading.

Reading a math book is not like reading other types of books. I recommend that you read the article "How to read a math book" by Stan Brown. This article gives some good specific tips on how to (and how not to) read a math book.

In order to get ready for the day's discussion, you should be prepared to summarize in your own words the main points from the reading. What is the overall theme of the reading? What are the main ideas, results, definitions, examples, and methods from the reading? What questions do you have from the reading? You may find it helpful to keep a reading journal similar to your lecture notes from your other classes.

HOMEWORK: To go with the reading, I will assign exercises on a daily basis in lecture. Assignments will also be listed below. Much of the next class meeting will be based on individual presentations of solutions to assigned exercises. Your participation score for that day will be based in part on your ability and willingness to present your own solutions, so you must keep up with the assigned exercises.

I will select several exercises each week for which you are to submit written solutions. These exercises will be assigned in class on Fridays and solutions will be due at the beginning of class on the following Friday. Assignments will also be listed on the course webpage. Each week's written assignment will be worth the same amount. I will drop your two (2) lowest homework scores. Late assignments will not be accepted.

You are encouraged to work on assignments in small groups, but each member of the class is required to turn in a neatly written, organized set of solutions, written in their own words. You will receive no credit for solutions with no work or justification. Pages should be stapled with "fringe" removed. I reserve the right to deduct points for messy papers.

ATTENDANCE: It is in your best interests to attend all class meetings. Good attendance is critical to your success in the class for a number of reasons. First, attendance and participation are worth 25% of your course grade. This will be measured by your presence in class and your willingness and ability to discuss the daily reading and to present solutions to assigned exercises. Second, your presence, attention, and participation in lecture will greatly help your performance in this class. For these reasons, I will take attendance each class period. Officially excused absences will not be counted against you, but you must document such situations with me personally.

EXAMS: Midterm exams will be taken in class and will last 50 minutes. The final examination will be comprehensive and will last 2 hours and 15 minutes. You will be allowed to use one (1) page of notes during each exam. Books and calculators will not be allowed during the exams. Make-up exams will not be allowed. If you have a conflict with the final exam date, you are responsible for making alternative arrangements with me beforehand.

TENTATIVE SCHEDULE: I reserve the right to make reasonable changes to the schedule if I find it necessary.

Martin Luther King, Jr. Day holiday: Mon 15 Jan
Last day to withdraw from courses before grade of ``W'' is assigned: Sun 28 Jan
Midterm 1: Fri 23 Feb
Last day to withdraw from courses with grade of ``W'': Sun 25 Mar
Spring recess: Mon 26 Mar to Sun 01 Apr
Midterm 2: Fri 06 Apr
Remembrance Day (this class will meet): Fri 04 May
Classes end: Fri 04 May
Final Exam: Wed 09 May, 10:15-12:30

COURSE NOTES: Clear and thorough notes from readings and discussions will provide you with a basis for your homework assignments and exams. You are responsible for taking notes during class, as I will not make course notes publicly available.

WORKLOAD: You should plan to spend 10--15 hours per week working on this course outside lecture.

ANNOUNCEMENTS: Course announcements will be sent to your email account. It is your responsibility to check this email account regularly.

GRAPHING CALCULATORS: Graphing calculators are not required for this course, but you may find one useful. (I personally use the TI-85.) Calculators will not be allowed in the quizzes or exams.

QUESTIONS: If something said or written in class is unclear, raise your hand and ask a question. I will try to clarify the point being made.

GROUP STUDY: Find at least one person in the class with whom you can study. Not only does this help you study better, but also, in the event you miss a lecture, you can get the notes and assignments from this person.

OFFICE HOURS: Come to my office hours for help. This gives me the opportunity to focus on specific problems you may be having and to explain things in a more personal manner. If the scheduled times are bad for you, make an appointment with me.

INSTRUCTOR FEEDBACK: Here is a link to an anonymous evaluation form where students can submit comments or suggestions for me at any time during the semester.

COURTESY: Cellular telephones, pagers, and other similar devices are not to be used and are to be turned off or set to vibrate-mode during class-time. Students violating this policy will receive one warning per semester. After the warning, violations will result in loss of attendance credit for that day.

STUDENTS WITH DISABILITIES: University policy 3342-3-18 requires that students with disabilities be provided reasonable accommodations to ensure their equal access to course content. If you have a documented disability and require accommodations, please contact the instructor at the beginning of the semester to make arrangements for necessary classroom adjustments. Please note, you must first verify your eligibility for these through Student Accessibility Services (contact 330-672-3391 or visit for more information on registration procedures).


PART I: Elementary Concepts
1. Numbers, Sets and Functions (5 days)
2. Language and Proofs (5 days)
3. Induction (4 days)
4. Bijections and Cardinality (5 days)

PART II: Properties of Numbers
5. Combinatorial Reasoning (2 days)
6. Divisibility (2 days)
7. Modular Arithmetic (2 days)
8. The Rational Numbers (5 days)

PART IV: Continuous Mathematics
13. The Real Numbers (2 days)
14. Sequences and Series (3 days)
18. The Complex Numbers (3 days)

STATEMENT ON ACADEMIC DISHONESTY: Excerpted from the University's Administrative policy and procedures regarding student cheating and plagiarism. Policy #3342-3-07
(A) Policy statement. It is the policy of the university that:
(1) Students enrolled in the university, at all its campuses, are to perform their academic work according to standards set by faculty members, departments, schools and colleges of the university; and
(2) Cheating and plagiarism constitute fraudulent misrepresentation for which no credit can be given and for which appropriate sanctions are warranted and will be applied.
(B) Intent and scope of the policy.
(1) In providing this policy, the university affirms that acts of cheating and plagiarism by students constitute a subversion of the goals of the institution, have no place in the university and are serious offenses to academic goals and objectives, as well as to the rights of fellow students.
(2) It is the intent of this policy to provide appropriate sanctions, to provide fair and realistic procedures for imposing those sanctions, to provide safeguards for any student suspected of cheating or plagiarism, and to coordinate the policy with procedures of the code of student conduct, rule 3342-4-15 of the Administrative Code and of this register.
(3) This policy applies to all students of the university, graduate and undergraduate, full or part-time, whose conduct is of such a nature prohibited by the policy. Other offenses of a nonacademic nature are covered by the code of student conduct, rule 3342-4-15 of the Administrative Code and of this register.
(C) Definitions. As used in this rule:
(1) ``Cheat'' means intentionally to misrepresent the source, nature, or other conditions of academic work so as to accrue undeserved credit, or to cooperate with someone else in such misrepresentation. Such misrepresentations may, but need not necessarily, involve the work of others. As defined, cheating includes, but is not limited to:
(a) Obtaining or retaining partial or whole copies of examination, tests or quizzes before these are distributed for student use;
(b) Using notes, textbooks or other information in examinations, tests and quizzes, except as expressly permitted;
(c) Obtaining confidential information about examinations, tests or quizzes other than that released by the instructor;
(d) Securing, giving or exchanging information during examinations;
(e) Presenting data or other material gathered by another person or group as one's own;
(f) Falsifying experimental data or information;
(g) Having another person take one's place for any academic performance without the specific knowledge and permission of the instructor;
(h) Cooperating with another to do one or more of the above; and
(i) Using a substantial portion of a piece of work previously submitted for another course or program to meet the requirements of the present course or program without notifying the instructor to whom the work is presented.
(j) Presenting falsified information in order to postpone or avoid examinations, tests, quizzes, or other academic work.
(2) ``Plagiarize'' means to take and present as one's own a material portion of the ideas or words of another or to present as one's own an idea or work derived from an existing source without full and proper credit to the source of the ideas, words, or works. As defined, plagiarize includes, but is not limited to:
(a) The copying of words, sentences and paragraphs directly from the work of another without proper credit;
(b) The copying of illustrations, figures, photographs, drawings, models, or other visual and nonverbal materials, including recordings, of another without proper credit; and
(c) The presentation of work prepared by another in final or draft form as one's own without citing the source, such as the use of purchased research papers.

Date Reading Assignment Exercises
01.19 pp. 2-6, 18-20 1.3, 1.7, 1.11, 1.20, 1.21, 1.30
01.22 pp. 6-10 1.14, 1.15, 1.33, 1.40, 1.41
01.24 pp. 10-14 1.45, 1.46, 1.47, 1.49, 1.50
01.26 submit 1.20, 1.21, 1.30
01.29 pp. 14-15 1.51, 1.52, 1.54
02.02 pp. 15-18 1.55, 1.56
02.05 pp. 25-31 submit 1.15, 1.40, 1.45(a), 1.46(a), 1.49(a,c), 1.50
02.07 2.3, 2.21, 2.23, 2.24
02.09 submit 1.51, 1.52, 1.54, 1.55
02.12 pp. 31-41
02.14 Snow Day
02.16 2.25, 29(a), 34, 37, 47, 48. (Also note 50 and 51.)
02.19 2.25, 29(a), 34, 37, 47, 48
02.21 Review for Midterm 1
02.23 Midterm 1
02.26 pp. 50-57
02.28 3.5, 3.10, 3.15, 3.21, 3.23
03.02 pp. 58-62 3.33, 3.41, 3.58(a)
03.02 submit 2.29(a), 2.34, 2.47, 2.48.
03.05 pp. 63-71 3.56, 3.63
03.09 submit 3.15, 3.21, 3.33, 3.41
03.12 4.1, 4.6, 4.11, 4.20, 4.22, 4.27
03.14 pp. 85-94
03.16 submit 3.56, 3.63
03.19 4.33, 4.34, 4.42, 4.43, 4.47, 4.49
03.26 submit 4.6, 4.11, 4.20, 4.27
04.09 pp. 100-110
04.11 5.21, 5.26, 5.30, 5.39
04.13 pp. 111-118 submit 4.42, 4.49
04.16 5.49, 5.50, 5.52, 5.58
04.18 Chapter 6
04.20 6.7, 6.8, 6.16, 6.28
04.20 submit 5.21, 5.39
04.23 6.18, 6.25, 6.34
04.25 pp. 139-149
04.27 submit 5.50, 5.52, 6.16, 6.28
05.04 submit 6.18, 6.25, 6.34 and proof of Lemma: If a,b,c are integers, then gcd(ca,cb)=|c|gcd(a,b).

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Last updated 26 April 2007.