Relearn, improve and filling gaps in Mathematics for University

Question

I know that several similar questions to this one have already been posted, but I can't find an answer that really suits me and my needs and after some research and reading I'm starting to feel quite desperate and lost, to the point that I don't really know which way to take or what to do.

This is my situation. I finished high school education eight years ago and I'm planning to go to University next September to study, if everything goes well, Physics. I'm preparing a couple of exams I need to pass (physics and chemistry) with my old textbooks and even if it's not everything I'd like to study, it's everything I need to focus on for the moment. But when it comes to mathematics I have a big issue. I know I'm going to need them for my degree, but I'm not quite worried about this particular thing because I'll deal with that during the course. The problem is that even though I've made some maths during these years just to spend some time I had, I feel (and know) that I'm quite rusted with the maths I once knew and that I have a lot of gaps in my knowledge of preuniversity mathematics. The point is that I'd like to prepare myself, to level up my maths, as well as fill as many gaps as I could have in my knowledge. In addition, since I feel also quite interested in maths themselves, I'd like to get a grip of general maths.

But I don't know what to do. I know some places, like Khan Academy, but I'm more the (text)book-oriented person.

I've been looking around and found several books, but I can't make up my mind about which ones to choose and start learning. I know that, I shouldn't be this picky or worry too much with such a basic knowledge I have and that almost everything should be good enough for me to start, but my time is limited, and so are my resources and means.

I know some trigonometry, algebra, analytic geometry and calculus (differentiation and integration).

Maybe a good way to start could be a book with lot of exercises to practice and review the things I used to know and to assess the things I don't know and so start working on them.

It's a triple problem: I don't know which things to study, since I ignore them, so I need some sort of way of figuring out what I ignore and need to study. I need to be prepared to deal with the maths I'm going to find during my degree. And I'd like to expand my knowledge of general maths.

So far, this is what I've found when it comes to books:

Geometry:

• Geometry: A High School Course, by Serge Lang.
• Schaum's Outline of Geometry

Trigonometry:

• Trigonometry, Corral
• Trigonometry, Gelfand

Precalculus in general:

• Precalculus Mathematics in a Nutshell, by Simmons

Algebra and general preuniversity mathematics:

• Schaum's Outline of College Mathematics
• Schaum's Outline of College Algebra
• Fundamentals of University Mathematics, McGregor

General mathematics:

• A Concise Introduction to Pure Mathematics, Liebeck
• What is Mathematics?, Courant and Robbins

I'd like to read and know about everything, but it's not about knowing, reading or collecting books, but about learning and going straight to the point. This is why I think I should try to avoid repeated subjects (even if repetition is basic for learning).

And when it comes to fields or topics, I think I'd need to work on the following:

• Geometry
• Trigonometry
• Algebra
• Probability, combinatorics and statistics.
• Some calculus and linear algebra.
• Proof, sets, concepts of mathematics.

I also know some places on the Internet:

• Paul's Notes (I've already gone through the College Algebra, but it's too elementary and easy).
• Khan Academy (I learnt a lot in the past, but I see it more like a complement to the actual learning through books, exercises and readings).
• Math is fun
• Purplemath

But I don't think it's a good idea to go jumping from one page to the following, skimming through their content just to learn an isolated bit of information.

I've wasted too much time all these years, and I know I may never be able to make up for lost time, but at least I'd like to be as prepared as I could, without unnecessary stress and overworking.

For my degree I would add some books on mathematical methods for Physics, but I need not worry for that right now, as I said above.

What do you think about Schaum's Outlines?

What do you think I should do? To try to go straight to the point and to focus on the main and most basic concepts?

Any advice will be helpful.

Many thanks.

Answer 1

(If this is not helpful, let me know and I can delete it. This post is about what math you will be doing) (If someone who does physics sees something that not totally representative of the math used in undergraduate physics, let me know)

I don't know what curriculum you need, but do have an idea of what you will need to know (now and in the future) for physics.

For basic physics (Like algebra based high school physics), you actually need to be familiar with algebra and trigonometry. So if you feel good about general physics, then you are probably not bad in these areas. One thing that could be good is to see if you can understand how the equations given are derived.

Most of what you do in physics mathematically will be calculus. You will need to know how to take derivatives and integrals, multivariable calculus, and to solve differential equations (ODEs and PDEs). You also will need to know linear algebra. However, you will learn a lot of this in the math classes that you will take. However, you will probably start in a calculus based physics.

For now, I don't think that probability is essential for your physics. However, you will probably need it to graduate and I think you need to understand it for quantum mechanics.

Do you know what kind of math courses you will be starting with?

Answer 2

Schaum's outlines are a great point to perform problem solving skills. However, as you progress in your studies, Schaum's is a little " light " on explaining the root concepts. This will leave you feeling vulnerable, especially when it comes to solving word problems. Because you'll find it difficult to understand the basic concept necessary to formulate a plan & equation to solve the problem. The supplemental material that you specified is adequate for your task. Please also consider reviewing principles that you don't fully understand, after reading about it, by watching " The Organic Chemistry Tutor " on YouTube. Take heart, you are not alone. I'm doing the same thing myself for actuarial science. Good luck and stay the course!

Answer 3

You don't have time review everything and none of us can predict exactly what you will need. I suggest you start by reviewing the calculus you have taken. It is basic for physics and for much of mathematics. Try to understand concepts that you didn't really get the first time. Work lots of problems. When they require algebra, geometry, trigonometry, or analytic geometry that you have forgotten go back and review what you need.

When you start your college classes you will need to learn to focus on the new topics that are presented, perhaps with a degree of concentration you did not always bring to your high school studies. Focusing on calculus and the related topics that arise there will be good practice for that. Also, you can probably benefit from some sense of solid accomplishment. You are more likely to get that benefit if you focus on calculus as the core and don't make yourself frantic by trying to do 'everything'.

My more opinionated advice, with which others here may disagree, is to stay away from Schaum's Outlines and stuff you find online. I grant that you could possibly get lucky and find something worthwhile there, but I'm guessing the average quality and applicability for what you need will be higher in a carefully written calculus book.

And when you get so exhausted working calculus problems that you can hardly think about math for the moment, then spend a bit of time pondering what a great and important step you are taking by starting college.