A Return to Mathematics: Algebra 1

mathdad

mathdad

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I took a break from math after turning 60 in April 2025. I did not plan to open another textbook for the rest of life. However, I miss math and textbooks. This time, I will go through the essentials of Algebra 1 through Precalculus.

If all works out in terms of reviewing important topics, I may even endeavor to step into Calculus 1, 2, and 3. I am waiting for my Algebra 1 to arrive in the mail. When the book arrives, I will return to this site for the purpose of posting math problems for discussion. I hope everyone is doing well.
 
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Beer drenched reaction follows.
mathdad said:
I took a break from math after turning 60 in April 2025. I did not plan to open another textbook for the rest of life. However, I miss math and textbooks. This time, I will go through the essentials of Algebra 1 through Precalculus.

If all works out in terms of reviewing important topics, I may even endeavor to step into Calculus 1, 2, and 3. I am waiting for my Algebra 1 to arrive in the mail. When the book arrives, I will return to this site for the purpose of posting math problems for discussion. I hope everyone is doing well.
Click to expand...
Good for you.
Also, welcome back.
I'm probably the only member here who hasn't turned on the Ignore feature on you yet.
Who knows? Well whatever; as I said, welcome back. Post whatever queries you may encounter in your textbook and let the learning (or games) begin. Them posts should only come after you think you you're already way beyond stumped. That way, any hint/suggestion or outright giveaway answer or even full blown solution to any problem exercise or any puzzling concept you encounter becomes a part of your eureka moment since it's already brewing in your mind. Subconscious assimilation usually works that way. Beer induced Subconscious assimilation works even faster; you might even like it if care to try it once in a while.

Btw, what book are you planning to use this time around? Sullivan's again perhaps? I read somewhere about Sullivan's 9th edition (2012) of Precalculus getting good reviews.
Same deal with the 6th edition (2005) of Cohen/Lee/Sklar's Precalculus: A Problems-Oriented Approach and the
7th edition (2012) of Cohen/Lee/Sklar's Precalculus.
Equally excellent is Ron Larson's 8th edition (2011) of Algebra & Trigonometry and Ron Larson's 9th edition (2014) of Precalculus. You might want to try any one of them excellent books.
 
jonah2.0 said:
Beer drenched reaction follows.

Good for you.
Also, welcome back.
I'm probably the only member here who hasn't turned on the Ignore feature on you yet.
Who knows? Well whatever; as I said, welcome back. Post whatever queries you may encounter in your textbook and let the learning (or games) begin. Them posts should only come after you think you you're already way beyond stumped. That way, any hint/suggestion or outright giveaway answer or even full blown solution to any problem exercise or any puzzling concept you encounter becomes a part of your eureka moment since it's already brewing in your mind. Subconscious assimilation usually works that way. Beer induced Subconscious assimilation works even faster; you might even like it if care to try it once in a while.

Btw, what book are you planning to use this time around? Sullivan's again perhaps? I read somewhere about Sullivan's 9th edition (2012) of Precalculus getting good reviews.
Same deal with the 6th edition (2005) of Cohen/Lee/Sklar's Precalculus: A Problems-Oriented Approach and the
7th edition (2012) of Cohen/Lee/Sklar's Precalculus.
Equally excellent is Ron Larson's 8th edition (2011) of Algebra & Trigonometry and Ron Larson's 9th edition (2014) of Precalculus. You might want to try any one of them excellent books.
Click to expand...
I am not going to start with Precalculus or College Algebra. I am doing a self-study or review of courses taken back in my school days. To construct a decent math background, returning to my high school 9th grade math class material (Algebra 1) is a good idea. I plan to complete the high school math program taken from 1980 to 1984.

Here are the courses that I plan to revisit using the Cliffs Review books:

•Algebra 1
•Algebra 2
•Geometry
•Trigonometry

This should give me a solid foundation to then proceed with the following courses using Michael Sullivan textbooks:

•College Algebra
•Precalculus

If I do well in all the above courses, I will finally endeavor to step into Calculus l, ll, and Ill using textbooks by the late James Stewart.

I will search for exams online for self-testing after completing each chapter. I think 20 questions of 5 points each per chapter exam is a good way to measure progress. What is the passing grade per chapter exam?

Let me see:

There are 20 questions. In NYC, the passing grade for exams as I recall is 65%. I will raise the passing grade to 70% in my self-study. So, 14 x 5 = 70. I will need to score 14/20 correct answers on each exam to successfully move on to the next chapter. The 14/20 objective allows me to get 6 wrong answers and still pass each chapter exam. Of course, the goal is to score higher than 70% but that is the passing grade for my self-study journey.

I will only post questions on this website after trying several times or when I need clarification on a certain idea, theory, etc. My goal is not to become a math "expert" or to become a math tutor or teacher or professor, etc. That would be ridiculous at age 60.
When people start aging, solving crossword or seduko puzzles is recommended to help keep memory power alive and well. Although I like crossword and seduko puzzles, nothing tops answering math questions as I travel through each chapter/each book.

Lastly, I simply want to review the essentials of the courses listed above. Cliffs Review books or the Math for Dummies series is a perfect collection of books for my goal. There's no need for me use traditional, thick, heavy textbooks like they do in colleges and universities at this time.

I like Michael Sullivan and James Stewart but their textbooks are for students with a strong math background. This is why returning to the basics (Algebra 1) is the right road to take. However, I will tackle College Algebra and Precalculus later in my self-study using Michael Sullivan textbooks.

If I decide to finally step into a self-study of Calculus l, ll, and lll, then books by the late James Stewart is the right choice to make. Any tips to help in my self-study are welcomed. If you know a better way to review math concepts learned decades ago, I welcome this as well.
 

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mathdad said:
I will search for exams online for self-testing after completing each chapter.
Click to expand...
A good search key is "<name of the course> + exam/test/problems + solutions + pdf". You can omit solutions if you like, but I would always add "+ pdf". It makes sure that you are more likely to end up on a university server somewhere on the globe rather than someone's private homepage.
 
fresh_42 said:
A good search key is "<name of the course> + exam/test/problems + solutions + pdf". You can omit solutions if you like, but I would always add "+ pdf". It makes sure that you are more likely to end up on a university server somewhere on the globe rather than someone's private homepage.
Click to expand...
Thanks for the tips.
 
mathdad said:
I took a break from math after turning 60 in April 2025. I did not plan to open another textbook for the rest of life. However, I miss math and textbooks. This time, I will go through the essentials of Algebra 1 through Precalculus.

If all works out in terms of reviewing important topics, I may even endeavor to step into Calculus 1, 2, and 3. I am waiting for my Algebra 1 to arrive in the mail. When the book arrives, I will return to this site for the purpose of posting math problems for discussion. I hope everyone is doing well.
Click to expand...
In my opinion, the best self-study books are "McGraw-Hill Schaum's Outline Series Collection". These books give you a plethora of Worked out examples. However, these books (in my opinion) are not very good at developing theorem. But you want to practice problems - these books are excellent for "review" topics (not first introduction to the subject/topic). These are available in the most bookstores/library as used books in a college/university.
Good luck
 
There is always still OpenStax from Rice University: https://openstax.org/subjects/math.

The pdf are free, and I think they have an option for printed versions at low costs. The books are, in my opinion, written for kids to bridge the various, very different school levels throughout the country, with what is necessary to start a study or enter college. I wouldn't use them for a mathematics study, but they are a good basis to start with.
 
khansaheb said:
In my opinion, the best self-study books are "McGraw-Hill Schaum's Outline Series Collection". These books give you a plethora of Worked out examples. However, these books (in my opinion) are not very good at developing theorem. But you want to practice problems - these books are excellent for "review" topics (not first introduction to the subject/topic). These are available in the most bookstores/library as used books in a college/university.
Good luck
Click to expand...
I find that the Schaum's Outline Series comes with many typos. The books have hundreds of problems to work through but also errors and many wrong answers.
 
fresh_42 said:
There is always still OpenStax from Rice University: https://openstax.org/subjects/math.

The pdf are free, and I think they have an option for printed versions at low costs. The books are, in my opinion, written for kids to bridge the various, very different school levels throughout the country, with what is necessary to start a study or enter college. I wouldn't use them for a mathematics study, but they are a good basis to start with.
Click to expand...
I thank you for the link but I will stick with the Cliffs Quick Review books. Of course, at age 60, this is just for fun. I don't plan to make a living teaching mathematics. This is not the goal. It's too late for me to seek a teaching career nor do I have the energy to do so.
 
\(\displaystyle \bold{Quick \ exercise}\).

Solve the inequality.

\(\displaystyle x^2 - 10 > 3x\)

This problem was given to us in the first day of Calculus class. Our professor wanted to measure our precalculus skills. Believe it or not, all students failed to answer it.

Therefore, if you get it correctly from the first time, you are better than, say \(\displaystyle 30\) university students who were aiming for the Bachelor degree in that time.

\(\displaystyle \textcolor{indigo}{\bold{mathdad}}\), you may want to hear what comes next!

Our failure to answer this simple question tells you that you don't need to study Algebra, Trigonometry, and Geometry before Calculus.

\(\displaystyle \bold{Start \ Calculus \ first}\). When you struggle in some part, say this part is related to Trigonometry, go back to only this one thing in Trigonometry, study it, master it if needed, then go back and continue Calculus.

You don't need to learn all Algebra, all Trigonometry, and all Geometry before Calculus. The idea is just to study what you need, so these three subjects or more if needed will be like references, you go back and forth between them only on the thing that you are struggling at.

Many will not agree with what I am telling you. But why I am telling you this?

\(\displaystyle \bold{One}\)
Calculus is the most beautiful subject of all in mathematics. You have not studied it yet, so you have already missed half of your life. Life is too short, so at least enjoy the second half of it with Calculus.

\(\displaystyle \bold{Two}\)
Most of the other subjects, if not all, depend on Calculus. For example, physics subjects are beautiful because they are full of Calculus.

\(\displaystyle \bold{Three}\)
When you solve problems in any field, say, fluid mechanics, Calculus will always be the easy part in these problems but in the same time it is the most beautiful part.

The list is very long and I don't want to bore you. I just want to tell you that Studying doesn't depend on age and whatever your purpose is, just start it.

We, the [imath]30[/imath] students started the journey of Calculus while we weren't even able to solve a simple inequality. Don't be shocked if I told you that we are engineers now. And I am still solving Calculus and I will not stop in any single day.

\(\displaystyle \textcolor{blue}{\bold{Start}} \ \textcolor{red}{\bold{Calculus}} \ \textcolor{green}{\bold{first}}\).
 
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logistic_guy said:
\(\displaystyle \bold{Quick \ exercise}\).

Solve the inequality.

\(\displaystyle x^2 - 10 > 3x\)

This problem was given to us in the first day of Calculus class. Our professor wanted to measure our precalculus skills. Believe it or not, all students failed to answer it.

Therefore, if you get it correctly from the first time, you are better than, say \(\displaystyle 30\) university students who were aiming for the Bachelor degree in that time.

\(\displaystyle \textcolor{indigo}{\bold{mathdad}}\), you may want to hear what comes next!

Our failure to answer this simple question tells you that you don't need to study Algebra, Trigonometry, and Geometry before Calculus.

\(\displaystyle \bold{Start \ Calculus \ first}\). When you struggle in some part, say this part is related to Trigonometry, go back to only this one thing in Trigonometry, study it, master it if needed, then go back and continue Calculus.

You don't need to learn all Algebra, all Trigonometry, and all Geometry before Calculus. The idea is just to study what you need, so these three subjects or more if needed will be like references, you go back and forth between them only on the thing that you are struggling at.

Many will not agree with what I am telling you. But why I am telling you this?

\(\displaystyle \bold{One}\)
Calculus is the most beautiful subject of all in mathematics. You have not studied it yet, so you have already missed half of your life. Life is too short, so at least enjoy the second half of it with Calculus.

\(\displaystyle \bold{Two}\)
Most of the other subjects, if not all, depend on Calculus. For example, physics subjects are beautiful because they are full of Calculus.

\(\displaystyle \bold{Three}\)
When you solve problems in any field, say, fluid mechanics, Calculus will always be the easy part in these problems but in the same time it is the most beautiful part.

The list is very long and I don't want to bore you. I just want to tell you that Studying doesn't depend on age and whatever your purpose is, just start it.

We, the [imath]30[/imath] students started the journey of Calculus while we weren't even able to solve a simple inequality. Don't be shocked if I told you that we are engineers now. And I am still solving Calculus and I will not stop in any single day.

\(\displaystyle \textcolor{blue}{\bold{Start}} \ \textcolor{red}{\bold{Calculus}} \ \textcolor{green}{\bold{first}}\).
Click to expand...
1. Thank you for your insight and suggestion.

2. I can solve the inequality you posted even after more than a year without opening a math textbook.

3. What you say makes sense, total, perfect sense. Still, I enjoy all the math courses presented in school before Calculus l.

4. I would like to know what others here have to say about your suggestion.

5. Why do you disagree that reviewing math courses typically taught before Calculus l is a waste of time?
 
jonah2.0 said:
Beer drenched reaction follows.

Good for you.
Also, welcome back.
I'm probably the only member here who hasn't turned on the Ignore feature on you yet.
Who knows? Well whatever; as I said, welcome back. Post whatever queries you may encounter in your textbook and let the learning (or games) begin. Them posts should only come after you think you you're already way beyond stumped. That way, any hint/suggestion or outright giveaway answer or even full blown solution to any problem exercise or any puzzling concept you encounter becomes a part of your eureka moment since it's already brewing in your mind. Subconscious assimilation usually works that way. Beer induced Subconscious assimilation works even faster; you might even like it if care to try it once in a while.

Btw, what book are you planning to use this time around? Sullivan's again perhaps? I read somewhere about Sullivan's 9th edition (2012) of Precalculus getting good reviews.
Same deal with the 6th edition (2005) of Cohen/Lee/Sklar's Precalculus: A Problems-Oriented Approach and the
7th edition (2012) of Cohen/Lee/Sklar's Precalculus.
Equally excellent is Ron Larson's 8th edition (2011) of Algebra & Trigonometry and Ron Larson's 9th edition (2014) of Precalculus. You might want to try any one of them excellent books.
Click to expand...
Do you agree with logistic_guy's suggestion? Why? Why not?
 
fresh_42 said:
A good search key is "<name of the course> + exam/test/problems + solutions + pdf". You can omit solutions if you like, but I would always add "+ pdf". It makes sure that you are more likely to end up on a university server somewhere on the globe rather than someone's private homepage.
Click to expand...
Do you agree with logistic_guy's suggestion? Why? Why not?
 
khansaheb said:
In my opinion, the best self-study books are "McGraw-Hill Schaum's Outline Series Collection". These books give you a plethora of Worked out examples. However, these books (in my opinion) are not very good at developing theorem. But you want to practice problems - these books are excellent for "review" topics (not first introduction to the subject/topic). These are available in the most bookstores/library as used books in a college/university.
Good luck
Click to expand...
Do you agree with logistic_guy's suggestion? Why? Why not?
 
fresh_42 said:
There is always still OpenStax from Rice University: https://openstax.org/subjects/math.

The pdf are free, and I think they have an option for printed versions at low costs. The books are, in my opinion, written for kids to bridge the various, very different school levels throughout the country, with what is necessary to start a study or enter college. I wouldn't use them for a mathematics study, but they are a good basis to start with.
Click to expand...
Do you agree with logistic_guy's suggestion? Why? Why not?
 
mathdad said:
Do you agree with logistic_guy's suggestion? Why? Why not?
Click to expand...
I mainly disagree with this assessment.

You are not in a "typical" situation, so anything that starts with "normally" doesn't count. His opinion is quite calculus centristic, and "most beautiful" is nothing I would sign. You can pretty well learn, e.g., abstract algebra or any version of the many topological branches, without the necessity of calculus. And Galois theory is - to me - definitely more beautiful than epsilontics in calculus. I like abstract algebra more than calculus, and you don't need the latter to learn about the former.

The question to be answered should be what provides the most fun. I was a fan of classical geometry long before I learned to differentiate. Learn whatever is joyful, and if you get stuck or have questions, come here (or visit https://www.physicsforums.com/) and ask. Of course, there are preliminaries that should be learned first: inequalities, trig formulas, precalculus, etc. These are the same as basic multiplication and division. You need them like you need numbers for counting, and you don't want to learn that the sum of angles in a triangle is 180° again and again.
 
fresh_42 said:
I mainly disagree with this assessment.

You are not in a "typical" situation, so anything that starts with "normally" doesn't count. His opinion is quite calculus centristic, and "most beautiful" is nothing I would sign. You can pretty well learn, e.g., abstract algebra or any version of the many topological branches, without the necessity of calculus. And Galois theory is - to me - definitely more beautiful than epsilontics in calculus. I like abstract algebra more than calculus, and you don't need the latter to learn about the former.

The question to be answered should be what provides the most fun. I was a fan of classical geometry long before I learned to differentiate. Learn whatever is joyful, and if you get stuck or have questions, come here (or visit https://www.physicsforums.com/) and ask. Of course, there are preliminaries that should be learned first: inequalities, trig formulas, precalculus, etc. These are the same as basic multiplication and division. You need them like you need numbers for counting, and you don't want to learn that the sum of angles in a triangle is 180° again and again.
Click to expand...
I also do not agree with logistic_guy. I am not in a formal classroom setting. My school days ended in the Fall semester of 1993. So, a revisit to courses taken before Calculus makes sense to me.

I like the physics forum but they don't like me. I have been banned from there many times. I will stick to my original plan. Start with Algebra 1 and take it from there. I just don't have the needed time to cover every topic in typical textbook..
 
khansaheb said:
You were signed in this forum before under various names - and people started to ignore you. You forgot that - I suppose.....
Click to expand...
Definitely not. I never used another username here, nor was I even present before. I don't know who or why somebody should ignore me. I think you confuse me with @logistic_guy. I defended his participation, yes, but I am not him.
 
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