Math 347 — UIUC, Fall 2012

This page is maintained by Xiannan Li.

Logistics

Lectures

MATH 347 X1 at MWF 12:00-12:50 in 141 Altgeld.
MATH 347 F1 at MWF 2:00-2:50 in 149 Henry Bld.

Office hours

Office hours: from 4:00 - 5:00pm on Wednesday, 1:30-4:00pm on Thursday and 4:00 - 5:00pm Friday, or by appointment in 107 Altgeld Hall.

Extra office hours after the end of lectures: Dec 13th: 2-3:30pm, Dec 14th: 2:30-4pm, Dec 17th: 2:30-4pm.

Assignment submission

Math 347 assignments are due on Mondays at the beginning of lectures.

Course intent and content

This course provides an introduction to rigorous mathematical reasoning and writing and serves as a gateway course and prerequisite for many upper level undergraduate math courses such as Math 417 or Math 444. You will learn the fundamental concepts in mathematics such as sets, functions, relations, etc.; how to form a rigorous mathematical argument (a "proof"); and how to write up the argument in a clear and logically correct manner. Along the way we will explore a number of interesting areas of pure mathematics, and introduce you to a number of nice problems.

This course will be significantly different from freshmen math courses. The solutions to the problems will require more creativity and effort, and in particular, it will not be possible to succeed in this course merely by memorizing the techniques you see in class or in the textbook. To be able to solve the problems in this course, it is hightly recommended that you participate actively in lectures, and put in a lot of effort into solving the homework problems on your own before discussing with others.

We will definitely cover Chapters 1-4, Chapter 13, and half of Chapter 14 of the text. Depending on time, we may also cover about two more chapters chosen from the text.

Text

Mathematical Thinking, by D'Angelo and West. Written homework assignments and your independent reading will come primarily from this book.

Weekly written homework

The written homework will be a chance to work on problems independently. Be sure that your final write-up is clean and clear and effectively communicates your reasoning to the grader. In particular, proofs should be written in full sentences and contain all the necessary details.

You can discuss the homework problems with others, but you must write up solutions independently, on your own. This is important practice, and will help you do well in the exams in this course, and in your future math courses. No late assigments will be accepted; however, your lowest two homework scores will be dropped.

Weekly Reading

The goal of the weekly reading assignments is to help you learn and retain the material at this pace. It will also serve to develop your skills at reading a technical subject.

Exams

This offering of Math 347 has three 50 minute midterm exams and one 3 hour final exam. The midterms will take place in class. Information on exact locations and times, as well as sample exams, will be posted in the Announcements section.

Grading

Your grade will be computed by combining scores from your written homework, midterm exam, and final exam according to the following percentages:
Homework: 20%
Midterms: 15% each, 45% total
Final Exam: 35%

Resources

Office hours

You are welcome to bring any questions you have to office hours.

Classmates

You are encouraged to discuss questions you have about the class with other students. However, you must write up homework solutions independently.

Email

My email is xiannan "at" illinois.edu. I generally check emails every weekday afternoon.

Assignments

Homework assignments will be posted here.

Be sure to consult the syllabus for homework policies, especially with regards to collaboration, write-up standards and submission. Turn in homework at the beginning of Monday's lecture.

Assignment 1 (due Wednesday Sept. 5th): 1.4, 1.7, 1.8, 1.22, 1.25, 1.28. Do not use calculus to solve any of the problems.

Assignment 2 (due Monday Sept. 10th): 1.15, 1.30, 1.39, 1.41 b) and d).

Assignment 3 (due Monday Sept 17th): 2.5, 2.10 c),d) and e), 2.11, 2.18, 2.28, 2.44.

Assignment 4 (due Monday Sept 24th): 3.3, 3.10, 3.15, 3.22, 3.24, 3.26.

Assignment 5 (shorter due to Midterm, due October 1st): 3.8, 3.40, 3.44.

Assignment 6 (due October 8th): 3.56, 3.62, 1.46, 1.49b), d) e), 1.50, 1.51b).

Assignment 7 (due Oct 15th): 1.47a), 2.26, 4.5, 4.6, 4.13, 4.21 (For this problem, you need to prove the existence of a certain bijection - you can either define a function explicitly and prove that it is a bijection, or you can proceed by induction on n. For either method, looking at small values of n should be helpful.)

Assignment 8 (due Oct 22nd): 4.8, 4.10 (assume that the domain and target are both the real numbers), 4.11, 4.22, 4.24, 4.34.

Assignment 9 (due date extended to Oct 31 - shorter due to midterm): 4.43, 4.45, 4.49 (you may assume here that the given sets are mutually disjoint).

Assignment 10 (due Monday, November 5th): 6.2, 6.3, 6.7.

Assignment 11 (due Monday, November 12th): 6.8, 6.11, 6.17, 6.18, 6.23, 6.40.

Assignment 12 (due Monday, November 26th): 13.1, 13.5, 13.8, 13.11, 13.19, 13.20.

Assignment 13 (due Wednesday, December 5th): 13.6, 13.12, 13.25, 13.26, 13.30, 14.3.

Assignment 14 (last homework! Due Wednesday, December 12th): 13.29, 13.37, 14.4, 14.12, 14.14, 14.33.

Assigned reading

You should read the following sections in the book:
  • Preface for the student.
  • The first 3 sections of Chapter 1, and "How to approach problems" section in Chapter 1.
  • All of Chapter 2.
  • All of Chapter 3.
  • The fourth section of Chapter 1.
  • All of Chapter 4.
  • The first two sections of Chapter 6 (pg 123-129).
  • All of Chapter 13, as it is covered in class.
  • The first 3 pages of Chapter 14, the first two pages of the infinite series section (pg. 279), Lemma 14.27 and Example 14.28 (as it is covered in class).

Breaking news!

Important announcements will be posted here as they come up in class.

Midterm 1

Your first midterm will be held in class on Wednesday, September 26th, 2011. Here's a sample midterm from a previous year: Fall 2009 (note that the last question involves strong induction, which we have not covered). Here's another sample exam from last year: Fall 2011. I will cover this sample exam in class. We will discuss the contents of our midterm in more detail in class. I will have extra office hours on Tuesday Sept 25th from 1:30pm - 4:00pm.

Midterm 2

Your second midterm will be held in class on Monday, October 29th, 2012. Here is a Sample Midterm. This sample midterm is slightly more challenging than your real midterm.

Midterm 3

Your third midterm will be held in class on Monday, December 3rd, 2012. Here is a Sample Midterm.

Final Exam

Our final exams are decided by Registrar's.
Times:
347 F1 - 12/15/2012, 1:30-4:30pm, in our classroom.
347 X1 - 12/18/2012, 7:00-10:00pm, in our classroom.
Here's a sample final. Also, take a look at the two extra problems which I couldn't fit into the sample final.

Here are solutions to the problems I did not cover in class.
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