A Return to Mathematics: Algebra 1

[khansaheb]

The average lifespan for men in the United States is about 74 years

Incorrect. According to Google:

As of 2023, the average life expectancy for men born in the United States was 75.8 years.

Men aged 65 in 2023 could expect to live an additional 18.2 years on average, reaching an expected age of 83.2.

 

[Steven G]

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.

Passing a math course with a grade of 65% (or even 70%) and moving on to the next math course is the number 1 reason students do poorly in their math classes! You need to basically get 100% on your exams. Now if you don't, then you need to be able to say when you see the solution that of course that is how I should have solved it. NOT, oh I don't understand the given solution or I don't understand part of the solution. Please don't fall into this trap.

 

[JeffM]

This has been a long thread. I am not sure a different thought will help.

The reason to start with elementary algebra is that it is the easiest way to get an introduction to modern mathematics. (I admit geometry is a more historical way.) But elementary algebra is where you start to learn abstraction, idealization, and generalization. These are all stumbling blocks for people trying to get comfortable with mathematics, but until a student has some grasp on them, calculus or abstract algebra are likely to seem utterly mysterious.

There is a second reason why elementary algebra is a great starting place. We all learn about numbers and numerals at a very early age, and much of what we learn then is necessarily childish and must be refined. When I used to tutor adolescents studying algebra, I would find, for example, terrible confusion between concepts as distinct as numbers and numerals. The letters in elementary algebra take the place of numerals when (a) we don’t yet know which specific numbers are relevant (unknowns), or (b) when we want to talk generally about all the members of some class of numbers (variables). If you have trouble understanding how letters can effectively substitute for numerals, you will be utterly baffled by y’ = uv’ + u’v where letters represent functions, an even more abstract class of ideas.

I suppose that you can learn calculus without previously learning algebra or trig or logarithms, but I suspect that it will be a real slog.

 

[khansaheb]

I may be able to understand Calculus 1 material now but I seriously want to complete the Sullivan textbook for the purpose of review. I took a Precalculus course (MA172) in the Spring 1993 semester at Lehman College. I got an A minus in the course. The course was taught by a student in graduate school preparing for his Doctorate Degree in Mathematics.

Newyear is knocking on our door - string of posts - yet not a single one with a mathematical problem......