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I'm a math major and a magician. If you would like to, you could call me a math-magician because I solve math equations magically. :-P
Also, to fulfill my my very first assignment, I would like to...
Hello! My name is Alli and I am a Junior majoring in Mathematics-Secondary Education. I enjoy reading [especially the Twilight series =) haha], watching movies, playing soccer [when the weather is...
Andy Schultz is the professor for the course and the admin of this Wiki. Andy grew up in Texas and Mississippi before moving to Davidson, North Carolina for college. Despite his plan to major in...
Hi! I'm a math major with a minor in secondary education. I'm from a small town north-west of Chicago called Fox River Grove. In one more year I'll be student teaching! Wow…
I've done a lot of...
My name is Aviva Hana Calamaro, but I like to spell my middle name Hannah, so that both my first and middle names are palindromes. I'm junior in Mathematics and I am currently applying to graduate...
Here's a blank write-up page, just to get the category going.
My name is Brad Dorner. I am a junior math major, secondary ed minor, from Arlington Heights, IL. And no, I didn't go to the same high school as Rachel or Ted. I really enjoy watching baseball,...
Hi, my name is Brittney Scheeringa. I grew up on the South Side of Chicago (and no I'm not a Sox fan!). I went to an all girls school for high school and started my college volleyball career at the...
Hello all. My name is Carl and I'm a junior from Gurnee, Illinois, a north suburb of Chicago right near the border between Wisconsin and Illinois. I'm taking this class because I have for my...
The first chapter of the book introduces you to the basics of number theory, getting you comfortable with playing around with integers, introducing you to primes, and asking some basic questions...
Chapter 2 is all about modular (or congruence) arithmetic and how it can help us understand numbers and their properties. Here's the stuff we covered in class.
Lecture 6 - Modular Arithmetic
Today...
Chapter 3 develops the concept of an arithmetic function (pronounced "air - ith - meh - tick"), which we motivated by studying Euler's function. These functions are some of the most important —...
Chapter 4 is all about determining which numbers modulo p (where p is an odd prime) are actually squares of other numbers modulo p. This culminates in Gauss's amazing Law of Quadratic...
Chapter 5 is all about orders modulo m. The big theorem in this chapter is the theorem of the primitive element, which characterizes those moduli m for which a primitive root exists.
Lecture 22:...
The professor for this course — Andy Schultz — is available to talk to you about anything you'd like, pretty much whenever you'd like. His office is Room 238 of Illini Hall, and his office...
As we are all aware, there are plenty of numbers besides just the integers. Now is the time to bring this fact to the forefront. In this section, we will begin to explore the idea of continued...
Here we'll collect notes for all the lectures given in class.
Chapter 1
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Extra Material
Introduction
Cryptography is used to encode and decode information as a means of security. It’s used to hide messages from non-intended recipients by making the messages unintelligible to them....
Hello all. I'm currently a junior in math education and I want to teach high school after I graduate. I'm from a small town of about 900 people located in northwest Illinois. It is called Hanover...
Dennis Griffith is a senior in Mathematics and Computer Science from Olney Illinois. Next year he will be a Ph.D. student in Computer Science, either at UIUC or CMU.
To complete homework 0, an...
Lecture 27: Pythagorean Triples
Today's lecture was about Pythagorean triples.
Lecture 28: Math in Pop Culture
We started class by introducing the play Proof. Proof, written by David Auburn and...
The following problems are to give you practice for the upcoming midterm on the material which we've covered since the last homework assignment. These ideas will be covered on your test, so it is...
Today we started off the class by introducing what a Diophantine Equation is.
Diophantine Equations
Diophantine Equation
is any equation that contains one or more variables that can be solved in...
Summary
Today we introduced Goldbach's Conjecture and how it has been modified and verified to varying degrees since its inception in 1742. This includes the strong and weak versions of the...
Overview and Purpose
You and your team will be asked to prepare a project on a number theoretic topic of your choosing. The topic should be something which your team finds interesting and which you...
Hello, my name is Henry Chan, a sophomore mathematics major.
I enjoy solving mathematical problems.
My favorite problem I solved is:
Let and be positive integers. Show that if divides , then...
Hensel's Lemma
Let be an odd prime, , and such that and . Then the following statements hold true.
If and , then there is a unique integer such that and . Specifically, is determined by the...
Note: you should read the full assignment prompt before getting started.
Your 0th assignment is to create your own profile for the wiki; you should have this done by Thursday night. You can include...
This assignment is due by the beginning of class on Friday, January 30th. Be sure to review the homework guidelines before getting started.
Prove that for any and any positive integer k, at least...
This assignment is due by the beginning of class on Monday, April 27th. Be sure to review the homework guidelines before getting started.
Given a primitive Pythagorean triple, x, y, and z, prove...
This assignment is due by the beginning of class on Wednesday, May 6th. Be sure to review the homework guidelines before getting started.
Find all solution to .
Can 4385745 be expressed as a sum...
This assignment is due by the beginning of class on Friday, February 6th. Be sure to review the homework guidelines before getting started.
For each of the following, determine the number of...
This assignment is due by the beginning of class on Friday, February 13th. Be sure to review the homework guidelines before getting started.
From Strayer, Chapter 2, do the following...
This assignment is due by the beginning of class on Monday, February 23th. Be sure to review the homework guidelines before getting started.
From Strayer, Chapter 2, do the following...
This assignment is due by the beginning of class on Friday, March 6th. Be sure to review the homework guidelines before getting started.
From Strayer, Chapter 3, do the following...
This assignment is due by the beginning of class on Friday, March 13th. Be sure to review the homework guidelines before getting started.
From Strayer, Chapter 3, do the following...
This assignment is due by the beginning of class on Friday, March 20th. Be sure to review the homework guidelines before getting started.
From Strayer, Chapter 4, do the following...
This assignment is due by the beginning of class on Friday, April 3rd. Be sure to review the homework guidelines before getting started.
From Strayer, Chapter 5, do the following...
Mathematics is best learned by doing, so part of your responsibility in this class is to complete weekly homework assignments. The basic rules for submitting homework are:
Your assignment should...
If you are allowed to edit pages in this Site, simply click on edit button at the bottom of the page. This will open an editor.
To create a link to a new page, use syntax: [[[new page name]]] or...
As a means for creatively engaging with the course material, you'll be expected to make regular posts to the forum section of the course Wiki to record number theoretic ideas or conjectures which...
Hello Everyone!
My name is Jacqueline and I am a junior in math secondary ed from Orland Park, IL. I love to ski, travel, cook, run, and spend time with my family and friends. I like to watch...
My name is Jeff Hevrin and I am a junior in math (and hopefully with a minor in CS). I am from Normal, IL which is about 45 minutes from here (that's where ISU is at).
My favorite things to do...
My name is Jen and I'm a math major with a secondary education minor. I'm also going to add a Social Science: Psychology endorsement to my teaching certificate, so I'm really interested in that...
I'm a sophomore and a math major. So far I like it. I am applying to the secondary ed program because I want to teach. My hobbies include bad reality shows right now but I'm hoping that phase of my...
I am a senior math major and will be graduating after this semester. After school I am hoping to move to Colorado and spend a winter snow skiing before moving on with my life. My favorite slopes to...
In class on the first day we discussed how you should joint the wiki. The first step is to sign up for a wikidot account. Once this is done, you just need to type in the "secret password" below....
Joshua a senior in Mathematics. He was born in Chicago, but immediately moved and currently resides in the northwest suburb of Niles.
To pay for food, he works at Foellinger Auditorium and for the...
Hello!
My name is Katie Barratt and I am a senior Math major, and a Secondary Ed and Spanish minor. I love traveling, sleeping, coffee shops (preferably not-so cooperate ones), reading, eating,...
My name is Kevin Davidsaver, and I'm a senior majoring in math. I'm from Bishop Hill, Illinois originally and plan to go to grad school at some point, again to study math. I like algebra, also set...
I am a senior majoring in econ and math. However, before wanting to be an economist, I really wanted to be a pilot. That was until I stumbled across my sophomore year.
… and I cannot wait for...
Lance Barke is a Senior at the University of Illinois and came from the small town called Metamora. This town is near Peoria, Illinois which is about an hour and half away from Chambana. He took...
( 16 points) Complete the following sentences
Dirichlet's Theorem states…
For a given integer n, counts…
(15 points) Answer the following questions either “true” or “false.” If...
Summary
We started today by getting to know the policies and expectations in the course. All of this is available already on the syllabus, but if you have any questions don't be shy about...
Summary
We started today by finishing off the proof of Fermat's Little Theorem, then proceeded to use this theorem to give various properties which make life modulo p nice. In particular, we saw a...
Summary
We started today by looking for a generalization to Fermat's Little Theorem, and in doing so we conjectured what is known as Euler's Theorem. This theorem relates the number of residue...
Summary
In today's class we finished our discussion of Euler's function, particularly how one goes about computing for an arbitrary integer n. This left us considering a more general class of...
Summary
We started today by finishing a proof of a proposition mentioned last class period which lets us generate new multiplicative functions from old multiplicative functions. The benefit of this...
Summary
We started today's class with a little observation of how number theory creeps into our daily lives without our realizing. We then spent the lion's share of the class discussing the...
Summary
In today's class, we discussed perfect numbers: those numbers n so that . We gave a characterization of even perfect numbers and talked about properties that odd perfect numbers have —...
Summary
We started today's class by introducing a few new arithmetic functions. When then spent the balance of the class period defining convolution of arithmetic functions, viewing some of the...
Summary
In today's class we finished talking about convolutions, with the highlight being the proof and a few applications of the Mobius Inversion Formula. Afterwards we talked about quadratic...
Summary
In today's class we discussed some of the basic properties of quadratic residues. We then uncovered the Legendre symbol, exploring its connection to Euler's Criterion and using this to set...
Summary
In today's class we began by reviewing the criteria we saw for evaluating Legendre symbols last class period, particularly when the "numerator" was either -1 or 2. Afterwards we set to...
Summary
Today we continued our discussion of divisibility and its basic properties. We saw some examples of how to put these properties into practice to prove exciting new results which might...
Summary
In today's class we covered some applications of quadratic reciprocity, and in particular saw how it could be used to answer whole classes of quadratic congruence questions at once.
Some...
Summary
Today we proved Quadratic Reciprocity. We started by developing a cousin to Gauss' Lemma that's called Eisenstein's Lemma, and then used this lemma — together with a geometric argument...
Summary
We started the class by introducing the notion of order for a given integer a modulo m, as well as what it meant for a to be a primitive root modulo m. We calculated the order of a few...
Summary
In today's class we began by paying back some IOUs from last class, particular proving a lemma and a corollary which allow us to compute the order of a power of a once you know the order of...
Summary
In today's class we finished proving a critical result concerning the number of elements of order d modulo p, where p is a prime number. This let's us conclude that primitive roots do exist...
Summary
Today we proved the (majority of) the primitive root theorem, and so we are now able to determine exactly which moduli m have primitive roots. Indeed, this means we can count precisely how...
Summary
Today we covered the final topic of Chapter 5, and we spent the bulk of the day discussing the idea of index relatively to a given primitive root mod m. The index is akin to the logarithm...
Summary
We started class by introducing the play Proof. Proof, written by David Auburn and published in 2001, deals with three mathematicians: a mathematics Professor, his daughter, and his former...
Recap and Summary
Last class period we talked at length about divisibility and the division algorithm. Today we moved on to discuss the concept of greatest common divisors. We finished by...
Integers as Sums of Squares
Note: the information (except selected portions near the end) comes from our Text by Strayer
Introduction: We began by splitting the students into small groups, and...
Summary
Today we spent the first half of the class exploring questions about prime numbers. Along the way we proved that there are infinitely many prime numbers and that there are arbitrarily large...
Summary
Today we began by finishing off the proof of the fundamental theorem of arithmetic. After we completed the proof, we saw how the fundamental theorem could be used to facilitate the...
Summary
Today in class we introduced the notion of modular congruence and saw that it can be used to give an equivalence relation to the integers. Not only does this provide us with a way to split...
Summary
Today we started by reviewing how one can go about "canceling" common factors in congruence equations. Afterwards we introduced the notion of a linear congruence equation, giving a theorem...
Summary
We started off today by talking about a special class of linear congruence equations, namely those of the form . These led to multiplicative inverses, which we saw were useful in solving...
Summary
We started today by saying a few more words about techniques for solving CRT problems aside from the method developed in class last time. We then shifted gears; instead of trying to solve...
You can submit as many of the problems below as you desire to be graded for extra credit on the first exam. Your solutions must be submitted by the beginning of class on Wednesday, February 25....
Hi my name is Nick Baier. I am a junior in math and planning to double major in econ. I am planning on going into a graduate finance program for the trading of options and futures. My ideal goal is...
Maybe there's a faster way to do this, but here's what I thought about the integral we discussed yesterday, which was basically .
Notice that if the integral were instead , then we could use the...
Partition
Definition: A partition of a positive integer n is a way of writing n as a sum of positive integers.
Definition: An addend in a partition is called a part.
Example:
Partitions of 4:
4
3 +...
My name is Pichayoot Ouppaphan, or you can called me Ob for short. I'm a sophomore in computer science, and I'm thinking about getting a minor in Mathematics. I'm from Thailand.
I am interested in...
I'm a sophomore and a math major. So far I like it. I am applying to the secondary ed program because I want to teach. My hobbies include bad reality shows right now but I'm hoping that phase of my...
My name is Kevin Davidsaver, and I'm a senior majoring in math. I'm from Bishop Hill, Illinois originally and plan to go to grad school at some point, again to study math. I like algebra, also set...
My name is Richie. Currently a senior in Math. I want to teach high school math when I graduate.
I am a senior in Pure Math and am graduating this semester. I plan on going to grad school to become certified for secondary ed. I come from Northfield, IL, which is a suburb just north of Chicago....
Hey everyone! My name is Steph Matook. I am from Downers Grove (a suburb like most of you). I am a senior in the Math Education program and I have a minor in Spanish. I went abroad to Spain last...
If your team is able to come up with a topic on your own, that's great! Send me an email and I'll make sure that you "reserve" your topic. Project topics will be assigned on a "first come, first...
Wikidot uses a markup language called LaTeX to generate properly typeset mathematics. Since you'll be posting to the forum and creating Wiki pages with serious mathematical content, it's good that...
Hello fellow 'crazy' future math teachers! I'm really excited about teaching math and can't wait to get to know all of you- who knows some of us might end up teaching at the same school in the...
Overview
Today we provided an overview to the Riemann Zeta Function. We started by discussing the man of the hour — Bernhard Riemann. We then defined the Riemann Zeta function and performed a...
Hi! My name is Ryan, and I am a junior math major who is minoring in secondary education. I'm from Tinley Park, which is a southern suburb of Chicago. I'm usually kind of a quiet person, but that...
My name is Sasha Fajerstein and I am a junior undergrad student majoring in mathematics and minoring in secondary education. While I love math, my real passion is teaching. I love being around and...
Welcome to Math 453
How do I join?
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How do I typeset math?
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You were supposed to come up with a name on your own! Talk to your teammates and decide what page you'd like to create, then type
writeup:the_name_you_created
into the "add a new page" textbox...
Introduction
Number theory is the study of integers, primarily their structure under the operations of multiplication and addition. Though this seems a humble beginning, it is surprising how...
I am a junior in Mathematics and Secondary Ed and hope to be a high school math teacher and coach. I grew up in Arlington Heights a northwest suburb. I am hoping to teach in my old high school...
I am a junior in Mathematics and Secondary Ed and hope to be a high school math teacher and coach. I grew up in Arlington Heights a northwest suburb. I am hoping to teach in my old high school...
Give complete, concise answers to the following prompts. Be sure to include all hypotheses.
State either Gauss' Lemma or Eisenstein's Lemma; be sure to indicate which lemma you have chosen to...
There will be two midterms in the course and a final. The midterms are scheduled for February 25th and April 10th; if these dates change for some reason, you will receive at least 2 weeks notice....
Summary
Although we introduced the concept of greatest common divisors in class last time, we didn't come up with a very effective way of computing GCDs. We remedy this with the Euclidean...
Hey everyone. I'm a fifth year senior in Actuarial Sciences due to a couple major changes over the years. I'm from Naperville, Il and plan to up and move to Connecticut this summer. I also have...
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Coursenotes
Chapter 1
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Extra Material
Course...
SUMMARY:
We introduced today's lesson by showing a clip from the Simpson's involving the Pythagorean Theorem. Here is an excerpt from the clip.
Introduction:
Mr. Burns: Thank you for visiting our...
Introduction
This is the course Wiki for the Spring09 manifestation of Math 453, Section X13. This wiki can only be edited by members, which basically means students registered in the class. We'll...
According to Wikipedia, the world largest wiki site:
A Wiki ([ˈwiː.kiː] <wee-kee> or [ˈwɪ.kiː] <wick-ey>) is a type of website that allows users to add, remove, or otherwise edit...
