Course: MATH 2200, Section 001
Time/Place: M,W,F 9:40 AM - 10:30 AM; JTB 120
Instructor: Thomas Goller
Office Hours: Any time, by e-mail appointment, in JWB 307.
Homework 8 is due Monday, April 8. Make sure you have the final version of the notes!
Take a look at these solutions to Learning Celebration #4 .
4/3, 4/5: Read the introduction to Chapter 7, as well as 7.1 and 7.2. Here is the final version of the notes for the course , with Chapter 7 in its final form.
The review session for LC #4 will run on Friday, 3/29 from 2:30-4 PM in JWB 208. Come with questions!
My newest gift for you: solutions to Homework #7 .
3/29 right after class: Optional earlier date to do LC #4. We'll meet after class and I'll take you to the reserved room.
4/1: The fourth learning celebration! It will cover sections 4.4, 5.1, and 6.1-6.5. The main emphasis will be on proving claims by induction. There will be one problem asking you to run the Euclidean algorithm and back substitution and then use the resulting linear combination to solve a linear congruence. There will also be a problem or two on combinatorics, asking about permutations, combinations, and computations using the binomial theorem. To prepare for the questions on induction, do as many of the exercises in 5.1 as you can. To prepare for the questions on combinatorics, understand all the examples in the notes, do the exercises in Chapter 6 (there aren't very many), and compute some powers of binomials using the binomial theorem, as in Examples 6.4.3 and 6.4.4.
3/25, 3/27, 3/29: Read 5.2, 6.1, 6.2, 6.3, 6.4, and 6.5 (the sections in Chapter 6 are short). 6.6 is fun and optional. Here are the notes for the course with Chapter 6 in its final form.
Please peruse these solutions to Homework #6 .
Homework 7 is due Monday, March 25.
3/18, 3/20, 3/22: Read 4.4 and 5.1. Optional: read 4.5, which explains the RSA cryptosystem (I will not discuss 4.5 in class). Here are the notes for the course with Chapter 5 in its final form.
Ready for a spring break full of modular arithmetic? Homework 6 is due Wednesday, March 20, in class or by 5 PM in my office.
I give unto thee: solutions to LC #3 .
2/6, 2/8: Read 4.3. Do all exercises in 4.3! I'll post the homework assignment soon. Check your answers to computations using Wolfram Alpha. If you're still not feeling comfortable with computations modulo an integer, make up your own problems and check your answers using Wolfram.
The review for LC #3 will start at 2:30 PM on Friday in JWB 208. Come with questions!
Here are solutions to Homework #5 . Read at your own risk.
3/4: The third learning celebration! It will cover sections 3.2, 3.3, 3.4, 4.1, and 4.2. The format will be similar to previous LCs, except that there will be one problem asking you to run the Euclidean algorithm and back substitution, as in exercise 4.2.17. You should know how to prove that functions are injective or surjective, how to prove and disprove bijectivity, and how to prove basic facts about divisibility (as in HW 5).
2/25, 2/27, 3/1: Read 4.2. Do as many parts of exercise 4.2.17 as you need to be comfortable with the Euclidean algorithm and back substitution. If you want even more practice, choose additional pairs of numbers to your heart's content. Check that you're getting the right gcds (using prime factorizations and/or Wolfram Alpha) and that your linear combinations are equal to the gcds.
Enjoy these solutions to Homework #4 .
Number theory! Homework 5 is due Monday, February 25, in class or by 5 PM in my office.
2/20, 2/22: Read 4.1 and 4.2. Here's a version of the notes for the course with Chapter 4 in its final form.
Ladies and gentlemen! It is my great pleasure to present you with a refreshing Homework 4 , due Wednesday, February 20, in class or by 5 PM in my office!
2/13, 2/15: Read 3.5 and make sure you understand 3.1 through 3.4 as well. This material is fundamental to all of mathematics!
Here are solutions to Learning Celebration #2 . Go over these thoroughly!
For your pleasure: solutions to exercises in sections 3.3 and 3.4 . Try the exercises before looking at the solutions!
Here are solutions to Homework #3 . I'll post some solutions to exercises in 3.3 and 3.4 on Saturday evening. Try those exercises before looking at the solutions!
2/11: The second learning celebration! It will cover sections 3.1 to 3.4. The format will be similar to LC #1. You should know how to prove that one set is contained in another set, that two sets are equal, and that a function is injective or surjective, and you must be comfortable concocting counterexamples to claims involving sets and functions. This will probably be the most difficult learning celebration, since proofs involving sets and functions are difficult and you haven't had much practice yet. So be ready for a challenge!
2/06, 2/08: Read 3.3 and 3.4. Do all the exercises in 3.3 and 3.4 in preparation for the learning celebration on Monday. The most important exercises in 3.3 and 3.4 are 3.3.9, 3.3.10, 3.3.11, 3.4.8, 3.4.9, and 3.4.10, in which you can practice proofs involving injective and surjective functions. Also think about 3.2.8, 3.3.3, 3.3.7, 3.4.3, and 3.4.6.
Homework extension! Homework 3 is now due Wednesday, February 6, in class or by 5 PM in my office.
Here is Homework 3 , due Monday, February 4, in class or by 5 PM in my office!
Here are solutions to Learning Celebration #1 .
Go to the Undergraduate Colloquium on 1/30! Dan Ciubotaru will be talking about irrational numbers. See http://www.math.utah.edu/ugrad/colloquia.html for details!
1/30, 2/01: Read 3.1 and 3.2. Here's a version of the notes for the course with Chapter 3 in its final form.
1/28: The first learning celebration! Here are some notes to help you prepare: Notes on 2.6 .
1/23, 1/25: Make sure you have read all of Chapter 2, that you understand the three main types of proofs (direct, contraposition, and contradiction), and that you know how to prove logical equivalences. Go over Homework 2 and work on Exercises 2.6.1 and 2.6.2 in preparation for Monday's learning celebration!
Homework 2 is due Wednesday, January 23, in class or by 5 PM in my office!
1/14, 1/16, 1/18: Read Chapter 2 of the notes. I didn't make any changes to Chapter 2, so the version you already have is final!
Here is a rough course schedule . I'll try not to change the dates of the learning celebrations.
Here is Homework 1 , due Monday, January 14, in class or by 5 PM in my office!
1/7, 1/9, 1/11: Read Chapter 1 of the notes.
The syllabus has been updated with office hour information!
Here is a first version of the notes for the course . They are still a work in progress, particularly the later chapters. I'll post updated versions as the semester progresses.
The syllabus is up!
You do not need to buy any textbook for this course. We'll be following my discrete math notes, which I'll post online as a pdf. I'll post a syllabus soon.