Math 347: Fundamental Mathematics

Class info Lecture: MWF 3pm-3:50pm in 147 Altgeld Hall Deconfusion sessions: Tue 4pm-5pm in 2 Illini Hall Emergency info

Exams Midterm 1: Sep 30 (Wed), 3pm-3:50pm in 147 Altgeld Hall Midterm 2: Oct 28 (Wed), 3pm-3:50pm in 147 Altgeld Hall Midterm 3: Nov 18 (Wed), 3pm-3:50pm in 147 Altgeld Hall Final exam: Dec 17 (Thu), 7pm-10pm in 147 Altgeld Hall

Instructor info Name: Anush Tserunyan Email: anush at illinois dot edu Office: 369 Altgeld Hall

Final exam

• Time and place: Thursday (Dec 17), 7pm-10pm, in the usual classroom (147 Altgeld Hall)
• Extra office hours: Mon (Dec 14) and Wed (Dec 16) at 11:10am-12:00pm in my office (369 Altgeld Hall)
• Coverage: In short, everything we've covered this semester (minus a couple of small things). In detail:
  • Chapter 1: Sets, Functions, Inverse Image and Level sets
  • Not in the textbook: Image of sets under functions, i.e. the definition and properties of f(A) for a subset A of the domain of f.
  • Chapter 2: Quantifiers and Logical Statements, Compound Statements, Elementary Proof Techniques
  • Chapter 3: The Principle of Induction, Applications, Strong Induction
  • Chapter 4: Representation of Natural Numbers, Bijections, Injections and Surjections, Composition of Functions, Cardinality
  • Chapter 13: The Completeness Axiom (this includes sup and inf), Limits and Monotone Convergence (this includes the definition of eventually, as well as limit of sequences, bounded sequences, monotone sequences, etc.)
  • Chapter 14: Properties of Convergent Sequences, Cauchy Sequences, Infinite Series
• Practice problems for Chapter 14 (Last update at 9:47am on Dec 16: added the hypothesis of non-negativity in Problem 5.)
• Solutions to the practice problems for Chapter 14
• What your studying should include (but not be limited to): Carefully review all of the definitions and main/important theorems. Try to construct examples and non-examples for each definition and theorem. Redo the problems from all three Midterms as well as all three lists of practice problems. After solving them (or attempting to solve), carefully read my solutions to each Midterm as well as practice problems.

Midterm 3

• Coverage: Everything we've covered since Midterm 2. In the textbook, this corresponds to:
  • Chapter 4: Representations of natural numbers (i.e. the q-ary representations)
  • Chapter 13: The Completeness Axiom (this includes sup and inf), Limits and Monotone Convergence (this includes the definition of eventually, as well as limit of sequences, bounded sequences, monotone sequences, etc.)
• Practice problems for Midterm 3
• Solutions to the practice problems for Midterm 3
• Solutions to Midterm 3

Midterm 2

• Coverage: Everything we've covered since Midterm 1. In the textbook, this corresponds to the following sections in Chapter 4: Bijections; Injections and Surjections; Composition of Functions; Cardinality.
• Solutions to Midterm 2

Midterm 1

• Coverage: Everything we've covered up to (including) strong induction. In the textbook, this corresponds to:
  • Chapter 1: Sets, Functions, Inverse image and level sets
  • Chapter 2: All sections
  • Chapter 3: All sections
• Practice problems for Midterm 1
• Solutions to the practice problems for Midterm 1
• Solutions to Midterm 1

Homework

• When is it due? Homework will be assigned each week and collected on Wednesdays in class before the lecture starts.
• Will late homework be accepted? No. To deal with contingencies, the lowest homework score will be dropped (won't count towards the total homework percentage).
• Can we work in groups? Yes, in fact, it is very much encouraged! But, after a group discussion of solutions to the homework exercises, each student has to write them on his/her own in his/her own words. If two solutions are too similar, they will be disqualified.
• Homework format: Every homework assignment will consist of exercises from the textbook as well as not from the textbook (both equally mandatory).
• HW11
• HW10
• HW9
• HW8
• HW7
• HW6
• HW5
• HW4
• HW3
• HW2
• HW1

Office hours

Instead of holding office hours in my office, I will be holding weekly Deconfusion Sessions, during which I will just be in a classroom (to be posted above) for an hour and you can come ask questions or simply work on your homework. I encourage working in groups and having group discussions of problems. I will be there to help you when you get stuck. I strongly advise everyone to come even if they don't have any questions and even if they have fallen behind (the latter students can start reading the missed material and ask me questions about it while reading).

If you need to talk to me in private, email me to schedule an appointment.

Course material

• Textbook: J. P. D'Angelo, D. B. West, Mathematical Thinking: Problem-Solving and Proofs, Second Edition, Prentice Hall, 2000, ISBN 0-13-014412-6
• Course syllabus (topics and timetable)

Course logistics

• Grading scheme: total grade = homework 11% + midterms 3 x 18% + final exam 35%
• Where to look for your grades: All of your scores for homework and exams will be recorded on Moodle (learn.illinois.edu). Log in with your UIUC netID and click on Math 347.
• Letter grades: The final letter grade will be assigned based on the overall percentage obtained by the above grading scheme. The overall percentages will be curved in the very end of the semester, but no exam (midterms and final) will be curved individually.
• Letter grade distribution: Up to minor adjustments, the top 33% of students will get an A grade (including plus and minus), the middle 34% a B grade, and the bottom 33% a C grade and lower.
• Grading disputes: Regularly check your homework and exam scores on Moodle to verify that they are correct. Any grading complaints must be submitted within two weeks of the due date or exam date of the grade in question.

Advice on learning the material

Besides attending the lectures (which is absolutely crucial in succeeding in this course), I also strongly recommend reading the textbook after each lecture in order to thoroughly understand the material. Even if the material is exactly same as in the lecture notes, it is still good to see two different presentations.

The process of learning math happens by doing it, and not just reading or listening. This is why doing homework exercises are necessary to understand what's going on and internalize the material. I'll quote Paul Halmos here: Don't just read it; fight it! Ask your own questions, look for your own examples, discover your own proofs. Is the hypothesis necessary? Is the converse true? Where does the proof use the hypothesis? What happens in a special case?

See also this advice from one of the authors (D. West) of our textbook.