Pure Mathematics for Beginners –
Accelerated and Expanded Edition
Just 19.99 on Amazon

Hi everyone! Pure Mathematics for Beginners – Accelerated and Expanded Edition is now available in paperback from Amazon. Similar to its predecessor, this book was written to provide a rigorous introduction to Logic, Set Theory, Abstract Algebra, Number Theory, Real Analysis, Topology, Complex Analysis, and Linear Algebra. The book consists of 16 lessons. Explanations to all the problems in the book are included as a downloadable PDF file.

So, what do I mean by “accelerated and expanded” edition?

By “accelerated” I mean that the book covers most of the material from the standard edition within the first half of the book. For example, the first lesson on set theory now covers relations, functions and equinumerosity (in addition to all the basics). However, nothing is left out. Everything from the original edition is included. In fact, more exposition has been added to the original content, as well as more examples and additional clarifying remarks.

By “expanded,” I mean that a huge amount of additional content has been added to the book. In fact, most of the content in Lessons 9 through 16 consists of material that is not covered in the original edition (although some of the content can be found in my other books from this series such as Real Analysis for Beginners and Abstract Algebra for Beginners).

The paperback is now on sale on Amazon for only $19.99. Note that once the sale ends (in about 24 hours), the price of this book will go up to $64.99.

The promotion is now over. Thanks to all who participated. The book is available at Amazon here: Pure Mathematics for Beginners – Accelerated and Expanded Edition

You can get the solution guide in paperback here: Pure Mathematics for Beginners – Accelerated and Expanded Edition – Solution Guide (Note that you can download the solution guide as a PDF for free, but many readers prefer to have a physical copy of the solution guide.)

If you have any questions, feel free to contact me at the following email:

steve@SATPrepGet800.com 

Thank you all for your continued support!

A Trick For Free Two Day Shipping

I would like to finish this post with a little trick you can use to get free 2 day shipping on any of the books you decide to purchase without making any additional purchases. If you have never used Amazon Prime you can sign up for a free month using the following link.

Sign Up For Amazon Prime For Free

If you have already had a free trial of Amazon Prime you can simply open up a new Amazon account to get a new free trial. It just takes a few minutes! You will need to use a different email address than the one you usually use.

This next part is very important! After you finish your transaction, go to your Account, select “Manage my prime membership,” and turn off the recurring billing. This way in a month’s time Amazon will not start charging you for the service.

After shutting off the recurring billing you will still continue to receive the benefit of free 2 day shipping for one month. This means that as long as you use this new Amazon account for your purchases you can do all of your shopping on Amazon for the next month without having to worry about placing minimum orders to get free shipping.

Just be aware that certain products from outside sellers do not always qualify for free shipping, so please always check over your bill carefully before you check out.

Well I hope you decide to take advantage of this very special offer, or at the very least I hope you will benefit from my Amazon “free 2 day shipping trick.” Here is the link one more time:

Sign Up For Amazon Prime For Free

If you think your friends might be interested in this special offer, please share it with them on Facebook:

Thank you all for your continued support!

Solution Guide for Pure Mathematics for Pre-Beginners
Just 14.99 on Amazon

Hi everyone! I have just released the paperback version of a second solution guide from my Pure Mathematics series.

The paperback is now on sale on Amazon for only $14.99. Note that once the sale ends (in about 24 hours), the price of this guide will go up.

The book is available at Amazon here: Pure Mathematics for Pre-Beginners – Solution Guide

Please note that to get the full benefit from this solution guide, you should first purchase the book Pure Mathematics for Pre-Beginners. Also, note that at the present time this solution guide comes with the book Pure Mathematics for Pre-Beginners  as a free PDF download.

If you have any questions, feel free to contact me at the following email:

steve@SATPrepGet800.com 

Thank you all for your continued support!

A Trick For Free Two Day Shipping

I would like to finish this post with a little trick you can use to get free 2 day shipping on any of the books you decide to purchase without making any additional purchases. If you have never used Amazon Prime you can sign up for a free month using the following link.

Sign Up For Amazon Prime For Free

If you have already had a free trial of Amazon Prime you can simply open up a new Amazon account to get a new free trial. It just takes a few minutes! You will need to use a different email address than the one you usually use.

This next part is very important! After you finish your transaction, go to your Account, select “Manage my prime membership,” and turn off the recurring billing. This way in a month’s time Amazon will not start charging you for the service.

After shutting off the recurring billing you will still continue to receive the benefit of free 2 day shipping for one month. This means that as long as you use this new Amazon account for your purchases you can do all of your shopping on Amazon for the next month without having to worry about placing minimum orders to get free shipping.

Just be aware that certain products from outside sellers do not always qualify for free shipping, so please always check over your bill carefully before you check out.

Well I hope you decide to take advantage of this very special offer, or at the very least I hope you will benefit from my Amazon “free 2 day shipping trick.” Here is the link one more time:

Sign Up For Amazon Prime For Free

If you think your friends might be interested in this special offer, please share it with them on Facebook:

Thank you all for your continued support!

Solution Guide for Pure Mathematics for Beginners
Just 14.99 on Amazon

Hi everyone! Since the release of Pure Mathematics for Beginners, I have received many emails requesting that I release the solution guide for this book in paperback. I am happy to announce that a paperback version of this solution guide is now available.

The paperback is now on sale on Amazon for only $14.99. Note that once the sale ends (in about 24 hours), the price of this guide will go up.

The book is available at Amazon here: Pure Mathematics for Beginners – Solution Guide

Please note that to get the full benefit from this solution guide, you should first purchase the book Pure Mathematics for Beginners. Also, note that at the present time this solution guide comes with the book Pure Mathematics for Beginners  as a free PDF download.

If you have any questions, feel free to contact me at the following email:

steve@SATPrepGet800.com 

Thank you all for your continued support!

A Trick For Free Two Day Shipping

I would like to finish this post with a little trick you can use to get free 2 day shipping on any of the books you decide to purchase without making any additional purchases. If you have never used Amazon Prime you can sign up for a free month using the following link.

Sign Up For Amazon Prime For Free

If you have already had a free trial of Amazon Prime you can simply open up a new Amazon account to get a new free trial. It just takes a few minutes! You will need to use a different email address than the one you usually use.

This next part is very important! After you finish your transaction, go to your Account, select “Manage my prime membership,” and turn off the recurring billing. This way in a month’s time Amazon will not start charging you for the service.

After shutting off the recurring billing you will still continue to receive the benefit of free 2 day shipping for one month. This means that as long as you use this new Amazon account for your purchases you can do all of your shopping on Amazon for the next month without having to worry about placing minimum orders to get free shipping.

Just be aware that certain products from outside sellers do not always qualify for free shipping, so please always check over your bill carefully before you check out.

Well I hope you decide to take advantage of this very special offer, or at the very least I hope you will benefit from my Amazon “free 2 day shipping trick.” Here is the link one more time:

Sign Up For Amazon Prime For Free

If you think your friends might be interested in this special offer, please share it with them on Facebook:

Thank you all for your continued support!

Pure Mathematics for Pre-Beginners
Just 14.99 on Amazon

Hi everyone! Pure Mathematics for Pre-Beginners is now available in paperback from Amazon. This book, consisting of 8 lessons, provides an elementary introduction to pure mathematics. Explanations to all the problems in the book are included as a downloadable PDF file.

The paperback is now on sale on Amazon for only $14.99. Note that once the sale ends (in about 24 hours), the price of this book will go up to $44.99.

The book is available at Amazon here: Pure Mathematics for Pre-Beginners

If you have any questions, feel free to contact me at the following email:

steve@SATPrepGet800.com 

Thank you all for your continued support!

A Trick For Free Two Day Shipping

I would like to finish this post with a little trick you can use to get free 2 day shipping on any of the books you decide to purchase without making any additional purchases. If you have never used Amazon Prime you can sign up for a free month using the following link.

Sign Up For Amazon Prime For Free

If you have already had a free trial of Amazon Prime you can simply open up a new Amazon account to get a new free trial. It just takes a few minutes! You will need to use a different email address than the one you usually use.

This next part is very important! After you finish your transaction, go to your Account, select “Manage my prime membership,” and turn off the recurring billing. This way in a month’s time Amazon will not start charging you for the service.

After shutting off the recurring billing you will still continue to receive the benefit of free 2 day shipping for one month. This means that as long as you use this new Amazon account for your purchases you can do all of your shopping on Amazon for the next month without having to worry about placing minimum orders to get free shipping.

Just be aware that certain products from outside sellers do not always qualify for free shipping, so please always check over your bill carefully before you check out.

Well I hope you decide to take advantage of this very special offer, or at the very least I hope you will benefit from my Amazon “free 2 day shipping trick.” Here is the link one more time:

Sign Up For Amazon Prime For Free

If you think your friends might be interested in this special offer, please share it with them on Facebook:

Thank you all for your continued support!

Pure Mathematics for Pre-Beginners
Coming Soon

Today I would like to announce that I will be releasing my new book Pure Mathematics for Pre-Beginners shortly. This book was written in response to a small amount of feedback that I received from customers of Pure Mathematics for Beginners.

When I released Pure Mathematics for Beginners, the majority of the feedback I received was overwhelmingly positive. However, I quickly learned that the book was too difficult for some readers. I refer to these readers as “pre-beginners.” By a “pre-beginner,” I mean a student that is ready to start learning some more advanced mathematics, but is not quite ready to dive into proofwriting.

Pure Mathematics for Pre-Beginners will be released within the next month at a special promotional price.

To be added to the notification list, simply send an email to steve@SATPrepGet800.com with “Notify me” written in the subject line.

If you think your friends might be interested in being notified of this special offer, please share it with them on Facebook:

Thank you all for your continued support!

Boosting Your Extracurriculars:

7 Ways to Help Them Stand Out
for College Applications

by Padya Paramita, InGenius Prep

As you settle into high school, you should think about how to prepare yourself for the eventual college application process. Of course, you don’t have to get a head start on all of the components in ninth grade. But planning out your extracurriculars in a way that will later help make you memorable to admissions officers can go a long way toward boosting your application profile when the time comes. From leadership positions to demonstrating your commitment, here are some tips to guide you through building an activities list that will impress admissions officers at competitive colleges across the country:

• Build your management skills and seek out leadership positions – Colleges appreciate students who are not afraid to take charge. Rather than just joining clubs that all your friends are in so you can get more time to hang out, seek roles where you can actively build your leadership skills. If your achievements as a leader are quantifiable or tangible – such as successfully recruiting 20 new members to your club – that’s even better.

• Of course you can’t immediately be voted the president when you first join, but you can start to establish yourself as a leader. When you join a new club where you think you see yourself as the captain in a year or two, act accordingly. Assert yourself – promote projects, support the current president, volunteer to take on responsibilities, and grow into someone your fellow group members can rely on and respect. So by the time you’re running for president, everyone knows that you will make a great leader – because you already are.

• Think about your competition – The bottom line is, your extracurriculars must stand out in order to compete with your peers. While joining Debate Club or Model UN sounds cool on paper – and they do teach important skills such as public speaking and research – they are common activities that many, many students choose to pursue. When picking your clubs, ask yourself whether it’s an activity that would help distinguish you, or if it’s likely to make admissions officers say, “Oh! Another applicant in Debate Club!” You definitely don’t want to be in the latter pack. Strive for extracurriculars that can help you get an edge over other high schoolers.

• Start your own initiative – When it comes to making your extracurricular activities stand out, being the president of a pre-existing club isn’t always enough. For example, every high school has a Drama Club and every one of those groups has a president. So being the president of the Drama Club isn’t the most unique role, is it?

• In order to compete with top students from other schools, consider taking the initiative to start your own club, LLC, nonprofit, or project. Seize something you’re passionate about and run with it. If you’re obsessed with comedy and your school doesn’t have any comedic activities, start your own improv troupe. You don’t have to launch your own group immediately. But as time passes, you need to develop depth; start building your application profile and think about what kind of opportunities you feel your community might be missing.

• Involve others – If you’re starting a club and it has zero members, that won’t make the best impression on admissions officers at your dream university. Colleges look for students who aren’t afraid to work with others, grow as a team, and learn from their community. So if you start your own club, work on growing its membership. If you’re interested in engineering, perhaps you could form a group which helps new folks moving into your neighborhood carry and assemble their furniture. The possibilities to tie your interests to the people and communities surrounding you are endless.

• Participate in activities that reflect your passion – When you apply to college, try to maintain a clear theme for your application so admissions officers remember you. Your interests and future plans should align to a certain degree with your intended major, even though this may all change. Your extracurricular selection should also enhance this theme. For example, if you have stated on your application that your biggest passion is art and that you want to work as an artist in the future, admissions officers won’t take you seriously if your extracurriculars have all been science-related. Seek out activities where you get to explore your passion!

• Quality, not quantity – Students sometimes get the impression that colleges want to see you participate in as many activities as you possibly can. That isn’t necessarily true. If you’ve invested a lot of time starting one organization that’s successfully improved the lives of people in your community, this will be more likely to boost your college application instead of being a general member of ten different clubs that have no connection to each other.

• Like we’ve said, it’s more about how you’ve led different initiatives and focused on the tangible achievements. Colleges want to see students who spend their time wisely. Don’t run to different club sessions all day. Focus your energy into two or three connected activities and lead those groups the best way you can.

• Don’t drop out of many activities – Admissions officers at top schools want students who demonstrate a high level of commitment towards meaningful activities. Of course, when you’ve just started high school, it’s more than acceptable to try out different types of extracurricular activities and see which fit your goals, and which you enjoy the most. If you’re not authentic in your choices, you won’t have a good time.

• Once you’ve figured it out, drop a couple of clubs that you don’t have time or passion for. But don’t make a habit out of it. Schools will not be impressed if your activities list is full of clubs you’ve only participated in for short periods of time. Your ability to commit and discover what you love reflects well on your application, so you shouldn’t be dropping all of your extracurriculars after tenth grade!

When it comes to building a strong extracurricular activities list, it’s important to prioritize your passions, career interests, and ways to establish yourself as a leader. Prestigious colleges want to see concrete achievements and commitment towards activities you enjoy. And if you see a gap in the activities at your school or find an opportunity to involve a greater community, don’t be afraid to start your own initiative!

Special Offer – Pure Math Paperback Bundle

Many of our customers have been asking if it is possible to purchase several of our pure math books for beginners in paperback for a discounted price. To meet this demand, we are pleased to introduce a special promotional package that includes all five of our pure math beginner books for the price of just $179. Shipping and all other fees are included in this price. By purchasing all five of Dr. Steve Warner’s pure math books as a bundle, you will save 20%, as compared to buying the books individually. The books included in this special promotion are:

• Pure Mathematics for Beginners
• Set Theory for Beginners
• Topology for Beginners
• Abstract Algebra for Beginners
• Real Analysis for Beginners

Note that if you were to buy each of these books separately the total price would be $225, plus taxes and possibly shipping. By purchasing the books here you will get all three books in paperback for just $179. This is a 20% savings.

Due to the bulk discount on this special offer, all sales are final (no refunds).
Please allow up to 14 days for processing and shipping.

To place your order simply click the following button.

For more information about these books you can visit each book’s Amazon page by clicking each book image below:

If you have any questions or concerns please feel free to contact Dr. Steve Warner directly at

steve@SATPrepGet800.com

Thank you all for your continued support!

Abstract Algebra for Beginners
Just 14.99 on Amazon

Hi everyone! Abstract Algebra for Beginners is now available in paperback from Amazon. This book, consisting of 16 lessons, provides a rigorous introduction to basic and intermediate abstract algebra. Explanations to all the problems in the book are included as a downloadable PDF file.

The paperback is now on sale on Amazon for only $14.99. Note that once the sale ends (in about 24 hours), the price of this book will go up to $44.99.

The promotion is over. Thanks to all who participated.The book is available at Amazon here: Abstract Algebra for Beginners

If you have any questions, feel free to contact me at the following email:

steve@SATPrepGet800.com 

You can also view the full Table of Contents here: Abstract Algebra Table of Contents

Thank you all for your continued support!

A Trick For Free Two Day Shipping

I would like to finish this post with a little trick you can use to get free 2 day shipping on any of the books you decide to purchase without making any additional purchases. If you have never used Amazon Prime you can sign up for a free month using the following link.

Sign Up For Amazon Prime For Free

If you have already had a free trial of Amazon Prime you can simply open up a new Amazon account to get a new free trial. It just takes a few minutes! You will need to use a different email address than the one you usually use.

This next part is very important! After you finish your transaction, go to your Account, select “Manage my prime membership,” and turn off the recurring billing. This way in a month’s time Amazon will not start charging you for the service.

After shutting off the recurring billing you will still continue to receive the benefit of free 2 day shipping for one month. This means that as long as you use this new Amazon account for your purchases you can do all of your shopping on Amazon for the next month without having to worry about placing minimum orders to get free shipping.

Just be aware that certain products from outside sellers do not always qualify for free shipping, so please always check over your bill carefully before you check out.

Well I hope you decide to take advantage of this very special offer, or at the very least I hope you will benefit from my Amazon “free 2 day shipping trick.” Here is the link one more time:

Sign Up For Amazon Prime For Free

If you think your friends might be interested in this special offer, please share it with them on Facebook:

Thank you all for your continued support!

Abstract Algebra for Beginners
Table of Contents

Since the announcement that I will soon be releasing Abstract Algebra  for Beginners, I’ve had several requests for more information about the book. I decided to post he table of contents, so that you can see exactly what topics will be covered in the book.

Remember, to be added to the notification list, simply send an email to steve@SATPrepGet800.com with “Notify me” written in the subject line. Now, here is the full table of contents:

Lesson 1 – Sets and Subsets

Describing Sets
Subsets and Proper subsets
Basic Theorems Involving Subsets
Power Sets
Transitivity of the Subset Relation
Equality of Sets
Cartesian Products
Basic Set Operations
Properties of Unions and Intersections
Arbitrary Unions and Intersections
Problem Set 1

Lesson 2 – Algebraic Structures 

Binary Operations and Closure
Semigroups and Associativity
Monoids and Identity
Groups and Inverses
Rings and Distributivity
Fields
Vector Spaces Over Fields
Modules Over Rings
Problem Set 2

Lesson 3 – Relations and Partitions

Binary Relations
n-ary Relations
Orderings
Intervals
Equivalence Relations
Partitions
The Ring of Integers Mod n
Problem Set 3

Lesson 4 – Functions and Equinumerosity

Functions
Injections, Surjections, and Bijections
Inverse Functions
Composite Functions
Identity Functions
Images and Inverse Images
Groups and Monoids of Functions
Equinumerosity
Countable and Uncountable Sets
Problem Set 4

Lesson 5 – Number Systems and Induction

The Natural Numbers
Well Ordering and the Principle of Mathematical Induction
The Integers
The Rational Numbers
The Real Numbers
The Complex Numbers
Exponential Form of a Complex Number
Problem Set 5

Lesson 6 – Substructures

Structures and Substructures
Subspaces of Vector Spaces
Substructures Generated by a Set
Problem Set 6

Lesson 7 – Homomorphisms and Isomorphisms

Homomorphisms
Isomorphisms
Linear Transformations
Matrices
The Matrix of a Linear Transformation
Images and Kernels
Normal Subgroups and Ring Ideals
Problem Set 7

Lesson 8 – Number Theory

Divisibility
Prime Numbers
The Division Algorithm
GCD and LCM
Problem Set 8

Lesson 9 – Number Theoretic Applications

Cyclic Groups
Modular Arithmetic
Solving Linear Congruences
Problem Set 9

Lesson 10 – Quotients

Cosets
Quotient Groups
Quotient Rings
Quotient Spaces
Problem Set 10

Lesson 11 – Structure Theorems

Isomorphism Theorems
Fundamental Theorem of Finite Commutative Groups
Problem Set 11

Lesson 12 – Permutations and Determinants

Permutations on Finite Sets
The Alternating Group
Permutation Matrices
Determinants
Matrix Groups
Problem Set 12

Lesson 13 – Sylow Theory

Conjugacy Classes
Groups of Prime Power Order
Sylow Subgroups
Group Actions
Problem Set 13

Lesson 14 – Polynomials 

Polynomials Over a Ring
Polynomials Over a Field
The Division Algorithm for Polynomials
Principal Ideal Domains
Unique Factorization Domains
Polynomial Functions
Problem Set 14

Lesson 15 – Field Theory 

Field Extensions
Algebraic Elements
Field Extensions as Vector Spaces
Splitting Fields
Problem Set 15

Lesson 16 – Galois Theory

Field Automorphisms
The Galois Correspondence
Solvability
Problem Set 16

If you think your friends might be interested in this information, please share it with them on Facebook:

Thank you all for your continued support!

Abstract Algebra for Beginners
Coming Soon

Today I would like to announce that I will be releasing my new book Abstract Algebra  for Beginners shortly. This book was written to provide a rigorous but easy to follow introduction to the subject of Abstract Algebra.

The book will be released within the next two months at a special promotional price.

To be added to the notification list, simply send an email to steve@SATPrepGet800.com with “Notify me” written in the subject line.

If you think your friends might be interested in being notified of this special offer, please share it with them on Facebook:

Thank you all for your continued support!

Why Do We Use the Real Numbers?

Let’s quickly recall a few basic sets of numbers:

In particular, the set of rational numbers consists of all fractions, where the numerator (number on top) and denominator (number on bottom) are integers (and the denominator is not 0). Here are some examples of rational numbers:

If the denominator is 1, we will identify the rational number with the integer consisting of the numerator alone. If the numerator is 0, we will identify the rational number with the integer 0. For example, we have:

At first glance, it would appear that the  rational numbers would be sufficient to solve all “real world” problems. So, why do we use the real number system? The real number system is so complicated to understand that teachers in elementary school, middle school, and even in high school do not even attempt to define it rigorously.

Well, it turns out that a long time ago, a group of people called the Pythagoreans showed that the rational numbers alone are actually not enough to solve all real world problems. The issue was first discovered when applying the now well-known Pythagorean Theorem.

The Pythagorean Theorem: In a right triangle with legs of lengths a and b, and a hypotenuse of length c, c² = a² + b².

Proving the Pythagorean Theorem is not too difficult and in fact, I have given an elementary proof here: Proving the Pythagorean Theorem

So, how does the Pythagorean Theorem tell us that the rational numbers are not enough? The answer lies in the following simple picture:

Question: In a right triangle where both legs have length 1, what is the length of the hypotenuse?

Let’s try to answer this question. If we let c be the length of the hypotenuse of the triangle, then by the Pythagorean Theorem, we have c²  = 1²  + 1²  = 1 + 1 = 2. Since c²  = c ⋅ c, we need to find a number with the property that when you multiply that number by itself you get 2. The Pythagoreans showed that if we use only rational numbers, then no such number exists.

Theorem: There does not exist a rational number a such that a²  = 2.

The proof of this theorem, although not too difficult, does require a bit of mathematical knowledge. Over the next few weeks, I will be teaching you the mathematics necessary to prove this theorem, with the ultimate goal of supplying a proof.

As it turns out, there is a real number a such that a²  = 2 (in fact, there are two such real numbers). In order to prove this, we would first need to give a rigorous definition of the real numbers. This requires a lot more work than one would initially expect.

The details of this definition are developed in my math books Pure Mathematics for Beginners, Set Theory for Beginners, and Topology for Beginners. These books contain no prerequisites and are perfect for anyone just starting out in theoretical math. You can get them all for one low price by clicking on the image below.