Prep for GRE® Subject Math Exam-Module6:Abstract Algebra

Name: Prep for GRE® Subject Math Exam-Module6:Abstract Algebra
Rating: 4.4 (47 reviews)

Solve GRE® subject math exam problems accurately and FAST!

Created byGilad Pagi

Last updated 7/2016

English

English [Auto],

What you'll learn

Excel in the GRE subject Mathematics exam's abstract algebra questions
Solve abstract algebra questions more quickly
Pace through the test

Course content

3 sections • 8 lectures • 1h 0m total length

Introduction0:50
Explore the abstract algebra module, partitioned into different modules including linear algebra and calculus topics, with reinforcement via UDMA courses; knowledge of a previous module is assumed.

Groups - Basics10:42
Define a group as a set with an associative binary operation, identity, and inverses. Identify subgroups, normal subgroups, and quotient groups, with examples like integers under addition and S3.
Zn Groups9:15
Examine Zn as an additive cyclic group of congruence classes modulo n, and apply gcd, Euclidean algorithm, and modular arithmetic to solve linear and diophantine equations.
Groups - Advanced11:57
Examine cyclic groups, generators via gcd with the order, and abelian classifications through direct sums of Z_p^k factors; contrast Z6 with Z2 ⊕ Z3 and explore nonabelian examples.
Rings, Modules, Fields, Maps8:52
Explore rings, modules, and fields, including identities, zero divisors, and units; understand homomorphisms, kernels, images, and isomorphisms, and how ideals form substructures.

Quiz15:27
Complete the final quiz by answering a few questions within two and a half minutes each, pace yourself, and note that answers appear in the next lecture.
Quiz - Answers2:22
Review of abstract algebra quiz questions on group homomorphisms, orders in Z_n, and generators in Z5. Apply isomorphism concepts, gcd reasoning, and modular arithmetic to determine correct answers.
Bonus Lecture1:30
Complete module 6 of the GRE subject math exam prep and practice with full exams. Access resources on the course website, including study plans, handouts, coupons, and a Facebook community.

Requirements

Be a math major in his/her senior year, or equivalent.

Description

This course is a prep course for the GRE Subject exam in Mathematics. If you wish to apply for a grad program in math, statistics and such, this exam is required.

This is the sixth module and includes all the abstract algebra material needed in order to excel in the exam. More importantly, the course teaches techniques for solving problems FAST (since in the exam you will have 2.5 min per question - very little time).

We will go over the following topics:

Group definitions
Equations modulo n
Group examples and operations.
Rings
Modules
Fields
Group homomorphism
Ring homomorphism

The course is designed to review all that is necessary to get you up to speed and get you solving real exam problems. Content covered in the previous modules is assumed.

See the free intro lecture to get more details.

GRE is a registered trademark of Educational Testing Service (ETS) in the United States and other countries. This content is not endorsed or approved by ETS.

Who this course is for:

This course is intended to prep for the GRE Subject Math test. NOT for the math section at the general GRE.
Students who wish to apply for graduate math programs must do the GRE Subject Math test. This course is designed for them
This course assumes knowledge equivalent to B.S in mathematics.
This course assumes knowledge of modules 1-5

Prep for GRE® Subject Math Exam-Module6:Abstract Algebra

What you'll learn

Explore related topics

Course content

General Information1 lecture • 1min

Abstract Algebra Theory4 lectures • 41min

Quiz3 lectures • 19min

Requirements

Description

Who this course is for: