Class times: 9:00-9:50 MTWT- 143 Henry Bld.
Instructor: Randy McCarthy, 324 Illini Hall, 244-7307, randy@math.uiuc.edu
Office hours: Friday, 9:00--9:50 in 324 Illini Hall
TA: Christopher Lee, crlee@uiuc.edu
Required Text: John P. D'Angelo and Douglas B. West, Mathematical Thinking: Problem-Solving and Proofs, 2nd Edition, Prentice Hall, 2000.
Prerequisites: Calculus II (Math 130 or 135 or the equivalent) and completion of the campus Composition I general education requirement.
Goals: This course prepares students for work in upper division mathematics courses by teaching selected fundamental topics from discrete and continuous mathematics, problem solving, techniques of proof, and clear mathematical exposition. Central goals of the course are to help students learn to read, construct and write mathematical proofs and to help students understand the structure and conventions of written mathematical arguments. Clear mathematical writing and clear mathematical thinking reinforce one another; for this reason, much attention will be given to the writing of mathematics.
Semester Schedule (subject to change):
| Class Meetings (MWT) | Topic |
| Part I Elementary Concepts | |
| #1-#3 | Numbers, Sets, and Functions |
| #4-#6 | Language and Proofs |
| #7-#10 | Induction |
| #11-#14 | Bijections and Cardinality |
| Part II Properties of Numbers | |
| #15-#18 | Combinatorial Reasoning |
| #19-#20 | Divisibility |
| #21-#23 | Modular Arithmetic |
| #24-#26 | The Rational Numbers |
| Part III Discrete Mathematics | |
| #27-#29 | Probability |
| #30-#32 | Two Principles of Counting |
| Part IV Continuous Mathematics | |
| #33-#35 | The Real Numbers |
| #36-#39 | Sequences and Series |
| #40-#43 | Continuous Functions |
Assignments: Homework will be assigned each week in lecture and will usually be due on Tuesday. It will be graded and returned. Homework assignments will consist primarily of writing mathematical arguments and proofs; the validity of the mathematical reasoning and the quality of the exposition will both count toward the grade. You are welcome to use any resources you like, including talking to one another. However, the more you can do on your own, the more you will learn. I strongly recommend that you put in some real work on a problem before consulting with anyone else. Also, each person must write up the work independently; doing otherwise will be considered plagiarism.
Goup Work: On Thursdays we will be working in small, randomly chosen groups. Problems similar to homework will be stressed. Each student is to turn in their own solutions. However, only one paper from each group will be graded and everyone in that group will receive that grade. In the unlikely event that one individual is clearly performing poorly relative to the others in their group an exception may be made to this policy. The Thursday group work will be counted towards your overall written work.
Additional writing assignments will be assigned in the weekly lab. See the summary below and the attached sample writing assignment for more details.
Topics for Tuesday Math 248 Lab/Discussion Sessions (subject
to change)
| Week 2 Jan. 28 | Introduction to TeX (mathematical word-processing software). Meet in Computer Lab, 108 Altgeld |
| Week 3 Feb. 4 | Peer review of written work. Students will work in groups, presenting their mathematical work and giving one another feedback on written drafts of the work. After the session, students will revise their drafts before submitting them. |
| Week 4 Feb. 11 | "Rules" of mathematical writing. Students will
discuss the conventions of mathematical writing in various settings and
compare these to the conventions of other types of writing.
Mathematical notation. Students will read and compare sample passages containing mathematical notation. Discussion of how the choice of mathematical notation affects the clarity of the writing. |
| Week 5 Feb. 18 | Peer review of written work. See Week 3. |
| Week 6 Feb. 25 | Peer review of written work. See Week 3. |
| Week 7 Mar. 4 | Test #1 |
| Week 8 Mar. 11 | Audience exercise. Students will compare several passages, all on a single mathematical topic, written for different audiences. |
| Week 9 Mar. 18 | Peer review. Students will bring to class a draft of an article written for a general (e.g. newspaper-reading) audience. In groups, students will discuss the drafts and give one another feedback. The students will subsequently revise the drafts for submission. |
| Week 10 Apr. 1 | Peer review of written work. See Week 3. |
| Week 11 Apr. 8 | Test #2 |
| Week 12 Apr. 15 | Peer review of written work. See Week 3. |
| Week 13 Apr. 22 | Peer review of written work. See Week 3. |
| Week 14 Apr. 29 | Paper-length writing. Students will discuss the conventions of mathematical writing of article length, having analyzed several examples in advance. This session will include practice in writing an abstract. |
| Week 15 May 6 | Test #3 |
Excused Absences: Acceptable reasons for excused absences are significant illness, family emergency, or University-sponsored travel. Whenever possible, you must notify me in advance, preferably in writing. In case of emergency, call me as soon as possible.
For an excused absence, you will be able to either make up the work or be excused from it - this is left to the instructor's discretion. For any foreseeable absence, the make-up work must be done in advance of the due date.
Exams: There will be three hour exams (Mar. 4, Apr. 8, May 6) and a comprehensive final exam (Sat. May 10, 8:00-11:00am). Notes and books may not be used on exams. You can use a calculator (up to TI-89) on exams. Because of the nature of the material, a calculator is unlikely to be of much use, however.
Grading: The course grade will be determined by
15% Exam 1
15% Exam 2
15% Exam 3
25% Final Exam
30% Written Work (including homework and additional writing assignments).
Plus/minus grades will be used in this section for the course grades.
General Education Credit: This course fulfills the Advanced Composition
general education requirement.