## Section 2.2: Modular Arithmetic

Given any set , where we define two operations: and . and

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# Math

## Section 2.2: Modular Arithmetic Analysis

## Hungerford’s Section 2.1

## Section 2.1: Congruence and Congruence Classes

## Prime Numbers

## Divisibility and the Euclidean Algorithm

## Sections 1.1-1.3

## My Introduction: Introduction to Abstract Algebra

Modular Arithmetic Analysis: It is clear that there are an n number of unique sets of Z_n but is there a way to calculate [a]*[b] without counting the final value of a*b and finding where that lies mod n? It’s very interesting that everywhere we look we can always find some sort of pattern. …

Hungerford’s Section 2.1 Analysis Thus far in Hungerford’s book I have yet to encounter something super difficult to understand. Proof techniques, of course, shall return to my memory as I study and practice but the material, especially in Section 2.1 is very straight forward. The most difficult part I have is trying to see how …

Congruence The concept of congruence initially may seem a bit confusing. I hope to explain the definition in a way that may be easier to understand. Definition of Congruence:

Primes As mentioned before: an integer is prime if the only divisors of said integer are ±1, or ± said-integer, but 0 and ±1 are not considered to be prime. (Think about it any integer divides

Divisibility To better understand divisibility I want to ask a question. Does a|bc imply a|b or a|c? The answer is no. A few counterexamples would be 6|4*3 but the following are not true 6|4 and 6|3.

Abstract Algebra Hungerford Section 1.1: The Division Algorithm Summary: Division is the repeated subtraction of a number there is a remaining value that is less than the number. This is idea is formally presented with the Division Algorithm

Hello World! I am a senior at Brigham Young University (BYU) studying physics. I’ve taken math classes up to Ordinary Differential Equations and here I start my study of Abstract Algebra (I will study Hungerford’s 3rd edition of his book entitled Introduction to Abstract Algebra). I realized a year ago that understanding physics well requires a firm …

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