# 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 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

## 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%