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!

Introduction to Pure Mathematics
for Advanced High School Students
Lesson 1 – Logic – Statements and Truth

Hi everyone! I have decided to create a series of math lessons in an attempt to expose advanced high school students to pure mathematics. I am making the first lesson available for free. Here are a few of the reasons I have decided to create these lessons:

• As a math professor, I have always found it to be unfortunate that most students that decide to become math majors are not exposed to real theoretical mathematics until their sophomore year of college.
• The high school curriculum in the US is full of computational math like algebra, trigonometry, and calculus. There is an extreme lack of pure mathematics being done in the classroom.
• How is a student supposed to know that they want to be a math major if they never have the opportunity to experience any pure mathematics? I hope to offer students the ability to give math a “trial run” before making an important life decision.
• Students who put in some time and effort to understand and solve problems in pure mathematics will improve their mathematical skill level much more than if they just complete nonrigorous high school mathematics such as calculus. This will have a real effect on their performance on standardized tests like the SAT and ACT, and their success in college.
• I hope that some high schools will eventually follow my lead and start offering a math course that gives an introduction to pure mathematics for their stronger math students that are considering becoming math majors.

The lessons I will be making available will cover topics in Logic, Set Theory, Abstract Algebra, Number Theory, Real Analysis, Topology, Complex Analysis, and Linear Algebra.

There are no prerequisites for using these lessons, although later lessons may require some knowledge from previous lessons. This does not mean that they are easy. Many of the problems included in these lessons require more advanced reasoning skills than any of the problem types done in typical high school math classes. Working through these lessons will help to develop those reasoning skills.

The first lesson that I have made available today covers basic sentential logic. The free version of this product includes a PDF file with notes followed by a problem set. The problems are broken down into five levels of difficulty. This product is available at my Teachers Pay Teachers store here:

Lesson 1 – Logic – Free Version

The paid version of this product (a small fee) also includes a second PDF file consisting of solutions to all the problems. The paid version can be found here:

Lesson 1 – Logic – Paid Version

After taking a look at the first lesson, I’d love to hear your feedback. Please feel free to email me with your comments and questions at steve@SATPrepGet800.com.

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

Thank you all for your continued support!

Important update: Once the 16 lessons were completed, I decided to put them all into a single book called Pure Mathematics for Beginners. You can find the complete book on Amazon here: Pure Mathematics for Beginners on Amazon

Gaining Mathematical Maturity

Today I would like to talk about mathematical maturity and how it relates to your performance on standardized tests such as the SAT, ACT, and GRE. Although there is no single agreed upon definition of mathematical maturity, I would define it as “one’s ability to analyze, understand, and communicate mathematics.”

There is no strict measure of mathematical maturity, but let’s examine what various levels of mathematical maturity might look like:

• Level 1: These students can do basic high school math when taught in a classroom setting. Students at level 1 can solve basic algebra and geometry problems by following the procedures that were taught to them. If such a student were asked, “Why does this work?” they will not be able to verbalize a satisfactory answer. Most high school students are at this level.

• Level 2: These students can learn basic mathematics without any outside help. Students at level 2 can read an algebra or precalculus book on their own  and can probably explain basic mathematics to other students. If shown how to do a problem, they will be able to solve problems that are similar using the same strategy. These students would have no problem in a Calculus course.

• Level 3: These students can learn advanced mathematics on their own. Students at level 3  can not only do problems, but can also explain why the methods they are using work. They can often solve problems in several different ways and develop their own techniques for solving problems. These students will be able to solve problems of a type that they have never seen before as long as they know the appropriate definitions and relevant background material.

These “levels” are just here to illustrate a point. It is often hard to pinpoint the exact level of a student. Some students naturally have a higher level of mathematical maturity than others. For example, students taking AP Calculus usually have a higher level of mathematical maturity than a student in remedial algebra. As such, the AP Calc student is more likely to do better in math on the standardized tests.

Simply knowing more mathematics is not enough to guarantee a higher level of mathematical maturity. An AP Calculus student does not have a higher level of mathematical maturity simply because they know more math. It is because they have been attempting problems that require a higher level of thinking.

The good news is that mathematical maturity can be increased. Doing so will greatly improve your problem solving ability as well as increase your math score on the SAT. Here are a few ways you can increase your level of mathematical maturity.

• Do SAT/ACT/GRE math problems. If you can currently only solve Level 1 geometry problems, and a month from now you can solve Level 2 geometry problems, then guess what—you have increased your level of mathematical maturity. So keep doing SAT (or ACT, etc.) problems a level above your current ability until the day of the test. If you have only about 3 months before your test, then this is the method you should employ most.

• Learn some mathematics by yourself. This may seem contrary to what has already been stated—but it is not. Knowing more mathematics will probably not raise your score very much, especially if the math is hand fed to you. But the process of learning mathematics will increase your mathematical maturity. What kind of math should you learn? It does not matter! Pick something you find the most enjoyable, and try to learn it on your own. If you get stuck, then ask for help—but developing the skill to learn math yourself will definitely increase your mathematical maturity. This strategy is more long term and you should consider it if you have 6 months or more before your standardized test. If the idea of learning advanced math on your own seems scary to you, you may want to check out my latest release – Pure Mathematics for Beginners. It’s perfect for anyone just starting out in theoretical math.

• Attempt difficult math problems. There are a lot of challenging math problems out there that only require the math that you already know. There are math magazines (yes, I know these sound like a lot of fun!), websites, and books full of problems. Pick a few and struggle with them. Just trying difficult problems and developing strategies will increase your mathematical maturity, even if you never solve a single one on your own. Also, solving problems using the advanced methods that are described in the many books I have written will boost your level of mathematical maturity.

I can still remember the day I got back my first real analysis homework as a first year graduate student at Rutgers University. I received a 62. This is by far the lowest grade I had ever received in mathematics. The worst part was that I had spent many hours on this homework, and I thought that it was completely correct. I remember approaching my teacher explaining that I never received such a low math grade, begging for him to tell me what to do. But he did not have an answer for me. I was on my own.

That whole first year of graduate school was a struggle. I wound up with B’s in most of my classes despite working harder than I had ever worked in my life. I was  unprepared for how difficult graduate school was, especially after receiving a 4.0 Math GPA as an undergraduate with very little effort.

This was quite disheartening and I thought that there was no way I would be able to do mathematical research and get my Ph.D. I just was not smart enough.

But an interesting thing happened during my second year. Apparently my hard work paid off. All of a sudden nothing seemed difficult anymore — I was back at the top of my class. Despite the fact that I was taking even harder classes than the previous year I was breezing through them with very little effort.

All of a sudden I was able to read advanced graduate texts on my own and do the problems at the end of each section without any help from others. What happened? Did I all of a sudden accumulate a massive amount of mathematical knowledge. The answer is no. In fact, this would not have helped. The mathematical language in my new classes was actually quite different from what I had learned the previous year.

What happened is that by struggling so hard the year before with little to no help from others, I managed to increase my level of mathematical maturity. Things that I did not stand a chance of understanding just a year earlier now made perfect sense. Other students were now coming to me for help, and I was able to help every single one of them. To think just a year earlier I was considering dropping out because it was just too hard. What a shame that would have been.

My level of mathematical maturity had to take several more jumps before I would graduate. Mathematical research is highly sophisticated and requires a clever mind that is willing to think in unconventional ways. The one thing that my years at graduate school have taught me is that anyone is capable of doing anything that they set their mind to.

Just don’t give up and you will persevere!

P.S. If you are preparing for a standardized test, you might want to take a look at the Get 800 collection of test prep books.

28 New ACT Math Lessons – Advanced Course
Just 19.99 on Amazon

Hi everyone! 28 New ACT Math Lessons – Advanced Course is currently half price on  Amazon. 

The paperback is now on sale on Amazon for only $19.99. Note that once the sale ends, the price of this book will go up to $39.99.

The promotion has ended. Thanks to everyone that participated. The book is available at Amazon for regular price here: 28 New ACT Math Lessons – Advanced Course

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 Beginners
Just 14.99 on Amazon

Hi everyone! Pure Mathematics for Beginners is now available in paperback from Amazon. This book provides 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.

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 $39.99.

The promotion is over. Thanks to all who participated. The book is available at Amazon here: Pure Mathematics for 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 Beginners
Coming Soon

Today I would like to announce that I will be releasing my new book Pure Mathematics for Beginners shortly. 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 will be released this week 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.

In the meantime, you can see what the first lesson looks like for free here: Lesson 1 – Logic

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!

48 New SAT Math Lessons
Just 7.99 on Amazon

Hi everyone! 48 New SAT Math Lessons is now available in paperback from Amazon. This book contains the 48 lessons from the first half of The Scholarly Unicorn’s SAT Math Advanced Guide. The book contains a total of 504 SAT math questions. Explanations to most of the problems are inside the book itself and the rest of the explanations are available as a downloadable PDF file.

Once again, this book does overlap with The Scholarly Unicorn’s SAT Math Advanced Guide, but it does not have any overlap with any of my other books.

The paperback is now on sale on Amazon for only $7.99. Note that once the sale ends (by this afternoon), the price of this book will go up to $34.99.

The promotion has ended. thanks to all who participated. Click the following link to get to the book’s Amazon page: 48 New SAT Math Lessons

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!

500 New SAT Math Problems
Just 5.99 on Amazon

Hi everyone! 500 New SAT Math Problems is now available in paperback from Amazon. This book contains the 3 problem sets from the second half of The Scholarly Unicorn’s SAT Math Advanced Guide. Explanations to the first 160 problems are inside the book itself and the rest of the explanations are available as a downloadable PDF file.

Once again, this book does overlap with The Scholarly Unicorn’s SAT Math Advanced Guide, but it does not have any overlap with any of my other books.

The paperback is now on sale on Amazon for only $5.99. Note that once the sale ends (by the end of today), the price of this book will go up to $34.99.

The promotion has ended. thanks to all who participated. Click the following link to get to the book’s Amazon page: 500 New SAT Math Problems

If you have any questions, feel free to contact me at 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!

SAT Math Classes

SAT math classes for the October exam are now available at a price of just $1400 per student. If you’re interested in both math and verbal, the fee is $2000. If you are interested in more detailed information, please email me at steve@SATPrepGet800.com

You can find more information about me and my company here: https://www.get800testprep.com/about

My Credentials

Here are some of my credentials:

• PhD in Mathematics
• 20+ years tutoring and teaching experience
• Author of more than 20 books for standardized test prep
• Many students with perfect scores on the SAT, ACT, and AP Calculus exams

My full resume can be viewed here: Dr. Steve Warner’s CV

My Classes and Current Rates

Aside from this one special class I am running, I am currently offering a 50% discount on private tutoring and a small discount on classes. Here is what I currently have available.

• SAT Full Prep Course – $2000
• SAT Math Prep Course – $1400
• ACT Math Prep Course – $1400
• AP Calculus AB Prep Course – $1400
• AP Calculus BC Prep Course – $1800
• GRE Math Prep Course – $1400
• Private tutoring – $250 per hour

Private tutoring is available for all of the following:

• K-12 mathematics
• all undergraduate math courses
• graduate courses in Mathematical Logic, Set Theory, Real and Complex Analysis, Linear and Abstract Algebra, and Differential Equations
• Standardized Test Prep in SAT, ACT, SAT Math Subject Tests, AP Calculus, GRE, GMAT, Math Regents

If you would like to discuss your needs for tutoring further, feel free to email me at steve@SATPrepGet800.COM or call me at 718-980-2935 and leave a message. I can usually get back to you within a few hours.

Thank you all for your continued support!

SHSAT Verbal Prep Book

Last year the SHSAT was changed significantly and this year it is changing one more time. The test will now have literature and poetry passages in the reading comprehension section. To make sure you are fully prepared, we have updated our SHSAT book by adding three literature passages and one poetry passage to the many passages already included in the book. You can find the latest version of the book on Amazon here: SHSAT Verbal Prep Book

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!

Introduction to Pure Mathematics
for Advanced High School Students
Lesson 1 – Logic – Statements and Truth

Hi everyone! I have decided to create a series of math lessons in an attempt to expose advanced high school students to pure mathematics. I am making the first lesson available for free. Here are a few of the reasons I have decided to create these lessons:

• As a math professor, I have always found it to be unfortunate that most students that decide to become math majors are not exposed to real theoretical mathematics until their sophomore year of college.
• The high school curriculum in the US is full of computational math like algebra, trigonometry, and calculus. There is an extreme lack of pure mathematics being done in the classroom.
• How is a student supposed to know that they want to be a math major if they never have the opportunity to experience any pure mathematics? I hope to offer students the ability to give math a “trial run” before making an important life decision.
• Students who put in some time and effort to understand and solve problems in pure mathematics will improve their mathematical skill level much more than if they just complete nonrigorous high school mathematics such as calculus. This will have a real effect on their performance on standardized tests like the SAT and ACT, and their success in college.
• I hope that some high schools will eventually follow my lead and start offering a math course that gives an introduction to pure mathematics for their stronger math students that are considering becoming math majors.

The lessons I will be making available will cover topics in Logic, Set Theory, Abstract Algebra, Number Theory, Real Analysis, Topology, Complex Analysis, and Linear Algebra.

There are no prerequisites for using these lessons, although later lessons may require some knowledge from previous lessons. This does not mean that they are easy. Many of the problems included in these lessons require more advanced reasoning skills than any of the problem types done in typical high school math classes. Working through these lessons will help to develop those reasoning skills.

The first lesson that I have made available today covers basic sentential logic. The free version of this product includes a PDF file with notes followed by a problem set. The problems are broken down into five levels of difficulty. This product is available at my Teachers Pay Teachers store here:

Lesson 1 – Logic – Free Version

The paid version of this product (a small fee) also includes a second PDF file consisting of solutions to all the problems. The paid version can be found here:

Lesson 1 – Logic – Paid Version

After taking a look at the first lesson, I’d love to hear your feedback. Please feel free to email me with your comments and questions at steve@SATPrepGet800.com.

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

Thank you all for your continued support!

Important update: Once the 16 lessons were completed, I decided to put them all into a single book called Pure Mathematics for Beginners. You can find the complete book on Amazon here: Pure Mathematics for Beginners on Amazon