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!

SAT and ACT Math Intensives

I am running 30 minute SAT and ACT math intensive sessions via live video (Zoom) at a very low price point (below $10 per session) for the duration of the Coronavirus outbreak. Each session will focus on problems from a specific topic and difficulty level.

The next session will be Sunday May 10, 2020 at 1 PM. The topic will be Graphs of Parabolas and it is intended for more advanced students. This session is appropriate for both the SAT and ACT. You can sign yourself or your child up for that class here:

SAT/ACT Math Intensive – Polygons

If you would like to be notified whenever a new SAT/ACT Math Intensive class is scheduled, please click the following link and enter your email address:

SAT/ACT Math Intensives – Notification List

I have also created video versions of my previous Intensive sessions. They are both intended for more advanced students and will be available only for a limited time. These topics are relevant for both the SAT and ACT. You can purchase access to the video intensive sessions using each of these links:

SAT/ACT Math Intensive – Graphs of Circles

SAT/ACT Math Intensive – Advanced Trigonometry

SAT/ACT Math Intensive – Graphs of Parabolas

Once you make each purchase, you will receive an email with the following:

• A printable PDF file with 10 questions
• A link to a video where I am providing complete explanations to all 10 questions
• Another PDF file with step-by-step solutions to all 10 questions

If you think that people you know might be interested in these intensive sessions for themselves or their children, please share it with them on Facebook:

Thank you all for your continued support!

SAT and ACT Math Intensives

I am running 30 minute SAT and ACT math intensive sessions via live video (Zoom) at a very low price point (below $10 per session) for the duration of the Coronavirus outbreak. Each session will focus on problems from a specific topic and difficulty level.

The next session will be Sunday April 19, 2020 at 1 PM. The topic will be Advanced Trigonometry and it is appropriate for both the SAT and ACT. You can sign yourself or your child up for that class here:

SAT/ACT Math Intensive – Advanced Trigonometry

If you would like to be notified whenever a new SAT/ACT Math Intensive class is scheduled, please click the following link and enter your email address:

SAT/ACT Math Intensives – Notification List

I have also created a video version of the first Intensive session. The topic of this session is Graphs of Circles and it is intended for more advanced students. This topic is relevant for both the SAT and ACT. You can purchase access to the video intensive session here:

SAT/ACT Math Intensive – Graphs of Circles

Once you make your purchase, you will receive an email with the following:

• A printable PDF file with 10 questions
• A link to a video where I am providing complete explanations to all 10 questions
• Another PDF file with step-by-step solutions to all 10 questions

If you think that people you know might be interested in these intensive sessions for themselves or their children, please share it with them on Facebook:

Thank you all for your continued support!

Three Things to Bear in Mind
When Shopping for Your
Dorm Room on a Budget

by Laura Pearson

Heading off to college is an exciting rite of passage for young adults. However, it can also be a trying time for some people. After all, you’re striking out into the world on your own, leaving behind the creature comforts of home to live in a space that’s likely smaller than what you’re used to and often shared with a veritable stranger.

Indeed, it can be quite a daunting paradigm shift, but the fact is that you can make the best out of your dorm room when you stock up on must-haves that make dorm life easier and more comfortable. Moreover, you don’t even need to empty out your student budget to get them when you can easily look for online deals, promo codes and coupons, and cashback specials offered by some sites to enjoy savings for anything from supplies to electronics. So, without further ado, here’s a guide on what stuff your dorm room should never be without.

To Save Space

No doubt, space is going to be your biggest challenge as you settle into your dorm room — especially if you have to share it with someone else. So, it’s more than wise to start your dorm room shopping with space-saving essentials.

While there are countless knick-knacks you can get to help you save space, it’s still best to limit your shopping to those you will use with some regularity. Tools that help organize and expand closet space are a must, such as organizing bins, hooks, and extension rods. You can also make use of the space under your bed with wheeled boxes and drawers, and perhaps even use bed risers to elevate your bed for precious additional inches. Other items like a wheeled cart, storage ottomans, and shoe and bed organizers are also great additions to this space. The best part is that most of these are available in dollar stores and won’t break the bank, so make sure to start your search in these stores first.

For Focus

Of course, don’t lose sight of the reason why you’re living in a dorm in the first place, and that is because you’re getting an education. For this reason, it’s very important to set up your dorm room as a space for learning with minimal distractions and better focus in mind—easier said than done, of course, especially in a shared room, but definitely possible in wallet-friendly ways.

First of all, you will need a desk. Most dorm rooms will already be furnished with one, but if yours isn’t (or the current one doesn’t pass muster), consider looking to the student marketplace in your school for a used one or venturing to online listings or flea markets in your area.

Next, organize your desk to keep clutter at bay, which can interfere with your focus. Again, you’ll want to raid your local dollar store or specialty shop for affordable desk caddies and organizers, drawer dividers, and a pinboard, to name a few. Again, such items won’t take up too much of your student budget, but do be more mindful as you shop so you don’t go overboard.

To Make It Feel Like Home

Finally, don’t forget to decorate your dorm room. More than just a place to sleep and study, it should also be a sanctuary of sorts for you, so you’ll want to strike a balance and make it homey, too. This can be done in cheap and easy ways. Consider getting linens that speak to your aesthetics and adding a cute throw pillow or two. You can also jazz up a blank wall by creating a photo mural or hanging posters, and maybe add a colorful rug to liven up the room. Again, do your due diligence before shopping so you can find the best deals both online and off.

Suffice it to say, dorm life is so much better when you have a space that you can love, appreciate, and really call your own. Thankfully, it’s not hard or costly to create one out of your standard-issue dorm room, so hop to it!

Photo via Pexels.com

SAT Math Intensive Video – Graphs of Circles

On Sunday, April 5, 2020, I gave my first SAT Math Intensive session. The feedback I received after the session was overwhelmingly positive. Therefore, I decided to create a video version of the session. The topic of this session is Graphs of Circles and it is intended for more advanced students. This particular topic is also relevant for those of you taking the ACT. You can purchase access to the video intensive session here:

SAT Math Intensive – Graphs of Circles

Once you make your purchase, you will receive an email with the following:

• A printable PDF file with 10 questions
• A link to a video where I am providing complete explanations to all 10 questions
• Another PDF file with step-by-step solutions to all 10 questions

If you would like to be notified whenever a new live SAT Math Intensive class is scheduled, please click the following link and enter your email address:

SAT Math Intensives – Notification List

If you think that people you know might be interested in these intensive sessions for themselves or their children, please share it with them on Facebook:

Thank you all for your continued support!

AP Calculus Information and Intensives

The upcoming AP exams will be unusual due to the Covid-19 outbreak. This year the exams will essentially be take home tests. The information I present here is specifically for the AP Calculus exams. You can find information on all the AP exams at the College Board’s website here: AP Exam Information

I’d like to begin with a short list of the most important things you should know about the AP Calculus exams this year:

1. Both AP Calculus exams will be administered on Tuesday, May 12, 2020 at 2 PM Eastern Standard Time.
2. Each test will consist of just two free-response questions.
3. You will have 30 minutes to complete and upload the first question (25 minutes to write your solution and another 5 minutes to upload your solution). This question will account for 60% of your grade.
4. You will have 20 minutes to complete and upload the second question (15 minutes to write your solution and another 5 minutes to upload your solution). This question will account for 40% of your grade.
5. Each question will require you to understand topics from at least two units.
6. A calculator is not required for either question. However, you may use a calculator if you wish.
7. Some topics that usually appear on the AP Calculus exams will be excluded. In particular, for the AB exam, you will not be tested on applications of integration. For example, you will not need to be able to compute any of the following: the area between two curves, cross sectional volumes, volumes of solids of revolution, average value over an interval, and other applications of integration.

To help students prepare for the exam this year, I will be running four 30- minute AP Calculus AB intensive sessions via live video (Zoom) at a price of $10 per session. The topics I have chosen are based upon what I have found that students have the most difficulty with and what I think is likely to appear on the AB exam. Here is the list of topics:

• Position, Velocity, and Acceleration
• Intermediate and Mean Value Theorems
• Related Rates
• Differential Equations

If you would like to be notified of these AP Calculus AB Intensive classes, please click the following link and enter your email address:

AP Calculus AB Intensives – Notification List

If you think that people you know might be interested in these intensive sessions for themselves or their children, please share it with them on Facebook:

Thank you all for your continued support!

SAT Math Intensives

I am running 30 minute SAT math intensive sessions via live video (Zoom) at a very low price point (below $10 per session) for the duration of the Coronavirus outbreak. Each session will focus on problems from a specific topic and difficulty level.

The first session will be Sunday, April 5, 2020 at 1 PM. The topic will be Graphs of Circles and it is intended for more advanced students. You can sign yourself or your child up for that class here:

SAT Math Intensive – Graphs of Circles

If you would like to be notified whenever a new SAT Math Intensive class is scheduled, please click the following link and enter your email address:

SAT Math Intensives – Notification List

If you think that people you know might be interested in these intensive sessions for themselves or their children, please share it with them on Facebook:

Thank you all for your continued support!

Mathematical Maturity and its Applications
to Standardized Test Preparation

What is mathematical maturity?

Before defining mathematical maturity, I should probably mention that there is no single universally accepted definition. If you ask two different mathematicians, “what is mathematical maturity?” you will probably get two different answers. One way that I like to define mathematical maturity is as the ability to analyze, understand, and communicate mathematics.

When I tell someone who I have just met that I am a mathematician, I will often get the response “I’m not a math person.” My personal belief is that there is no such thing as “math people” and “non-math people.” Each of us is just walking around with a different level of mathematical maturity. These “non-math” people simply have not had enough of the right kind of exposure to mathematics.

How can you determine your “level” of mathematical maturity?

Just like there is no single definition of mathematical maturity, there are not really well defined “levels” of mathematical maturity. You’ll never hear someone say “I have a level 2.7 mathematical maturity. What’s yours?” However, we can still describe what certain levels might look like.

For example, you have your typical high school student who can plug numbers into formulas and follow procedures to solve basic problems in subjects like algebra and geometry. Many of these students would not be able to explain where these formulas come from or why various procedures work to give you the correct answer.

A student at a slightly higher level might be able to learn some math on his or her own without the help of a teacher or tutor. They might also be able to apply techniques they have learned to problems somewhat similar to ones they have already seen.

Then you have students that can solve problems that they have not seen before by making connections to mathematics that they have already seen. These students can often solve problems in several different ways and can explain their methods to other students in an effective manner.

Is it possible to improve mathematical maturity?

It certainly is! No matter what level someone is at, it is always possible to improve that level further. I have improved my own level of mathematical maturity many times throughout my life. My most significant experience with mathematical maturity occurred when I began graduate school.

I remember handing in my very first homework assignment in graduate school. It was for my Real Analysis course. I was confident that I got everything right. Imagine my shock when I got my homework back with a grade of 62 out of 100. Not only did I get many of the answers wrong, but I didn’t even have the mathematical maturity necessary to realize that I didn’t understand what I was doing.

Throughout the rest of that first year of graduate school, I worked harder than I had ever worked in my life. Nonetheless, I could not get higher than a B in any class. As a student who received only A’s in my math classes as an undergraduate, this was devastating to me. I was actually thinking about dropping out of the PhD program.

Instead, I worked really hard the next summer to fill in all my gaps in knowledge and to work on really difficult math problems. I also sought out the smartest students in my classes to work with. What I lacked in knowledge and experience, I made up for with hard work.

Going into my second year of graduate school, I was terrified. I was about to take classes that were even more difficult than any class I had taken the previous year. However, something amazing happened. I found the classes to be very easy. I was now back to getting perfect scores on all my assignments and tests. Instead of asking other students for help, students were coming to me for help. Not only did I understand all the material, but I was able to explain it to others. Moreover, these classes were completely different from the classes I took the first year. This was when I realized that mathematical maturity was a real thing and more importantly, that it was possible to improve it.

How does mathematical maturity relate to standardized test scores?

For this section, my explanations will be in terms of the SAT, but anything I explain applies to just about any standardized test.

I once believed that every student had a maximum potential SAT math score that he or she could attain. For example, maybe a student is currently scoring 400 and with the right preparation, they can get up to around a 600. Therefore, they practice easy to medium difficulty questions and over a period of a few months, they work their way up to a 600.

What I have since realized is that mathematical maturity is the key to getting that “maximum” score even higher. In other words, a student’s “maximum potential” can be improved by increasing their level of mathematical maturity.

Just to clarify, an increased level of mathematical maturity will increase only the potential SAT score, not the actual score. To increase the actual score, one needs to prepare specifically for the SAT.

For example, let us take two students with current SAT scores of 400 and a maximum potential of 600 (we can pretend that these students are clones of each other – identical in every way). Suppose that one student spends a summer learning some Abstract Algebra, while the other does not do any math during that summer.

Now, suppose that both students begin preparing for the SAT at the same time for about three months. If they both attain their potential, the student that did nothing will get a 600. The student that studied Abstract Algebra, however, might get a 700 or even an 800. His maximum potential increased over the summer because he was working on improving his level of mathematical maturity.

What are some specific actions someone can take to increase their level of mathematical maturity?

Before providing specific methods, I think that it is important that I stress the fact that mathematical maturity cannot be improved overnight. The process of increasing one’s level of mathematical maturity requires patience and hard work. That said, here are three of my favorite methods:

• Learn some real mathematics. Pick up an advanced math book in a subject you are unfamiliar with and just start reading the chapters and working on the problems at the end of each section. Maybe try an Abstract Algebra book or book in Set Theory. I have actually written several pure math books on various topics designed to ease you in to the world of pure mathematics, while increasing your level of mathematical maturity (you can click on each image below to take you to the book’s Amazon page)

• Work on some challenging math problems in the subjects you already know. Look for problems from math competitions such as the Mathcounts exam (at a lower level) or the Putnam exam (at a higher level). You can also find challenging math problems in math magazines and other publications. Many such problems require only the most basic mathematics, and yet, they are still quite difficult. Struggle with some of these problems, even if you cannot get a single solution. The struggle will make you mathematically stronger.

 

• When preparing for a standardized test, go a bit “deeper.” In other words, instead of just answering a question, think a little more about what the question is asking. Try to solve each problem in more than one way. Think about why someone would ask this question. How does this question relate to other questions? Try to make connections between seemingly unrelated questions. As one specific example, questions about arithmetic sequences are often quite similar to questions involving linear equations (see the following post for details: https://satprepget800.com/2016/06/01/arithmetic-sequences-linear-equations-sat-act-prep/ )

Set Theory for Pre-Beginners
Just 14.99 on Amazon

Hi everyone! Set Theory for Pre-Beginners is now available in paperback from Amazon. This book, consisting of 8 lessons, provides an elementary introduction to set theory. 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: Set Theory for Pre-Beginners

I have also made the solution guide to this book available in paperback. You can get it here: Set Theory for Pre-Beginners – 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!

Set Theory for Pre-Beginners
Coming Soon

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

When I released Pure Mathematics for Beginners, the majority of the feedback I received was overwhelmingly positive. However, many high school teachers mentioned that the more theoretical aspects of the book were too much of a challenge for many of their students. I refer to these students 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.

Set Theory for Pre-Beginners will be released within the next 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.

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!

Pure Math Solution Guides Now Available in Paperback

Hi everyone! Readers of my “Pure Mathematics for Beginners” series have requested that I make the solution guides for these books available in paperback. I am happy to report that I have now done so for all five books in the series.

Please note that at the present time these solution guides comes with the books as free PDF downloads. However, since many of you have expressed that you would rather have these solution guides as a physical book, I have made these available for purchase.

For your convenience, each cover image below links to the Amazon page where you can purchase the book. If you would like to purchase more than three of these books at once, I would suggest that you contact me directly first. I may be able to get you a discounted price.

If you have any questions, I can be reached 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!