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The Math You Need to Learn Physics (Introductory Level)

  1. Apr 10, 2014 #1
    Hello everyone; hopefully the title was sufficiently descriptive. Essentially, I'm trying to learn physics. I've been looking through various college physics textbooks, and while some of the problems make sense to me, most of them don't, and I believe it is because I lack the foundation in the math. In fact, I often lack the foundation even in the algebra. I had a pretty poor math education throughout high school, which doesn't help matters.

    Anyways, I need suggestions for textbooks I should read to get a good ground in the math foundation before moving on to the physics. What algebra textbooks should I start with? Should I move on from reading algebra to trigonometry to calculus, or is there some specific sequence that is recommended? To give you an idea, I'm talking about the math you need to know for a typical first-year college physics course, and what textbooks you can find it in.
  2. jcsd
  3. Apr 10, 2014 #2
    Well, when I finished HS, my math skills were very poor. I started college with remedial math which equated to about 8th grade pre-algebra. I advanced through everything and am just about to pass University Calculus III and Physics II.

    I took pre-calculus while taking Intro to Physics, and I felt well equipped for the course.

    You need to find out where exactly your skills are at, usually texts have assessment chapters in the beginning - skills you should know before starting that book. Find an algebra text, try the assessment, and either start that book or find the book that precedes that book.

    basic algebra > Elementary algebra > intermediate algebra > college algebra > pre-calculus
  4. Apr 10, 2014 #3
    If you are planning to major in physics (or a similar field or want to learn what physics major learns) you will take a Calculus-based introductory physics course. This means, that up until this point you should have a solid grasp of elementary algebra (Algebra II is the high school course) and trigonometry. You can take calculus while you take the first introductory physics course and still get an A, but if you are self-studying physics I'd recommend at least learning the equivalent of a first-semester calculus course before trying to learn physics. A decent understanding of trigonometry is a prerequisite, and you should be able to do algebra flawlessly. This is true for both calculus and physics.

    For a small, concise, and quick book that will teach you high school geometry, algebra, and trigonometry in about 120 pages, I'd recommend

    Precalculus Mathematics in a Nutshell, by George F. Simmons.

    You can find it for $10 on Amazon.

    It covers:


    - Triangles, Circles, Cylinders, Cones, and Spheres


    - Basics (pre-algebra/algebra I stuff)

    - Functions and Graphs

    - Special Topics (Logarithms, Division of Polynomials, Systems of Equations, Sequences and Series, Permuations and Combinations)


    Now, the book does not have many problems, but it is very easy to find problems online. The explanations in the book might be to sparse if this is your first time learning these subjects, as well. I'd recommend using online sources like Khan Academy and PatrickJMT for good intuitive explanations. Just search on their youtube channels key words from the topic you're learning.

    Overall though, this book has every single topic I've learned in high school, and a few extras. If you are diligent with self-studying it works great, and it is to the point.
  5. Apr 17, 2014 #4
    I looked through the books by Simmons and solved some problems. I ordered some textbooks on Elementary and Intermediate Algebra, College Algebra, Trigonometry, and Physics and have been self-studying through the algebra textbooks. I answered almost all problems correctly and it seemed fairly straightforward.

    However, I went and took a math placement exam for school today and know I'm gonna end up being placed in the lowest category based on my score. After that test I was extremely depressed and discouraged. I mean, I want to study physics but I have to hope that you can improve your math skills based on practice. If I get placed in the lowest category, it's going to take me forever to graduate (and I'm not exaggerating when I say it's going to take way too long to graduate). I was going to try to take classes over the summer to help reduce the time it takes to graduate, but I don't think I can afford staying over the summer. I'm going to keep self-studying through the algebra textbooks.
    Last edited: Apr 17, 2014
  6. Apr 17, 2014 #5
    I would advise that you learn to appreciate first Physics but not to learn it with math straight ahead. Learn the concepts and admire the beauty of Physics. Take quantum physics for example, isn't it beautiful and so interesting that electrons can be at different places at once or pop out randomly from nowhere. You don't have to understand the math right away, but in knowing the beauty of its concept, one can appreciate it strongly than a person who jump straight ahead into math. As you can remember, and it is I think far more simpler than the modern scientific method, guessing is first, prior to calculating the consequences, then after those consequences the guess must agree with the environment, that is called experiment. Now, a brilliant scientist does not jump into a cliff of incomprehension, rather he approach it with a lot of contemplation and appreciation to the problem. This is exactly why I feel at contempt to schools, for inducing that science is about memorization rather than understanding first the concepts at hand.

    Then we are on the same boat. I hate high school so much because it only presents the concepts that I need to memorize and then grade me for not memorizing it. I don't care about memorizing the slope intercept form or the quadratic formula, instead present it to me why is it important? How does it apply to the natural world? Or even the most important question of all, What is mathematics? Then after that comprehension then the concepts of mathematics becomes intrinsic to our way of thinking because we understand it and appreciate it.

    Now with my advice, I am actually doing it right now, and I want to share it to my common fellows who experience the same thing. If you can't grasp algebra, study about arithmetic. If you can't grasp trigonometry, learn about algebra and geometry. If you can't grasp calculus, study algebra, geometry, and trigonometry. Know also that mathematics is not the same thing as physics, but what they do is to help one another. Know that mathematics, is a symbolic representation of the universe. It explains the universe through symbols as we call as numbers to quantify it or make exact measurements.

    Finally with the books, I advice old algebra books instead of modern ones since modern algebra books tend to be verbose while not explaining the importance of it. I would advise the series of books namely: Arithmetic for the practical man, Algebra for the practical man, Trigonometry for the practical man, Calculus for the practical man, all written by James Thompson, they are all available on the internet so just google them. I would advice learning arithmetic first and please do not tell me that you absolutely master it, cause I am willing to bet, and I maybe more likely to be false, that you don't know why arithmetic is important to algebra and that they are really just the same thing. So when learning I would advice is to be humble to yourself and learn the basics. Secondly, I would advise reading Euclid's Elements by Euclid to which is the Green Lion press edition.

    Other than that, cheers and good luck to us both!
    Last edited: Apr 17, 2014
  7. Apr 17, 2014 #6
    I appreciate the beauty of physics but I also understand that I need a lot more math before I can understand it conceptually. I obviously couldn't understand quantum mechanics with the level of math I'm at now. I can't even really understand classical mechanics besides at a very rudimentary level. As I said, I ordered two textbooks on physics, but I'm not really going to bother trying to seriously work through them until I get a much better grasp of the math.

    I understand what you're saying. I got good grades in high school math but my math education was horrendous. It was all rote memorization and no underlying explanation of the concepts.

    Alright, I'll look into those books as well. Right now, the books I've got:

    - Trigonometry by McKeague
    - College Algebra by Blitzer
    - Elementary and Intermediate Algebra by Dugopolski

    Right now, I feel very, very stupid, but I'll keep studying regardless.
    Last edited: Apr 17, 2014
  8. Apr 17, 2014 #7
    I don't think you understand what I am saying. I don't know calculus which is important in physics. But i don't need math to understand quantum physics, for I do understand it conceptually and comprehensively. Electrons when heated jumps out out of the said orbit and physicist call it the quantum leap. Do I need math to understand that? I don't know the exact reason why, but understanding its beauty and its importance is an overwhelming experience. Take it in step by step. Actually I envy those people who learned calculus at the very early age prior to college. But who cares? Knowing your own failures and incapabilities at a very early age is far more better than a person who thinks they will never fail. Being introduced to a humbling experience such as not knowing mathematics immediately is far more better than to be introduced to a delusion that success is an all perpetually pervading experience and failure will never visit you. Isn't it a better experience and whole lot story to tell one day, that I learned mathematics and physics on my own pure hardwork, on my own hard earned labor. But do understand that mathematics is important, and don't use this as a justification on not learning it on the future.

    If the young generation of today, thinks of physics as rather a complicated, sophisticated, and only the field of a genius and a brilliant intellect, I do worry about the future. How would we progress?
    Last edited: Apr 17, 2014
  9. Apr 17, 2014 #8
    Honestly, thats bull. You do need math to understand quantum physics. Math is the language of physics.
  10. Apr 17, 2014 #9


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  11. Apr 17, 2014 #10
    Yes, I do agree with Feynman, my dear sirs, but if you are just exposed to the concepts without the meaning of it, without the importance of it. How would it even occur to the mind of an aspiring physicist if you are just given the things to remember. I didn't say that math is not important it is! I even said that calculus is important to physics.
    And yes I do acknowledge my error saying physics can be understand without math it can't, all I'm saying is that physics should be appreciated first.
    Last edited: Apr 17, 2014
  12. Apr 18, 2014 #11
    Unfortunately, the position I'm at right now is where I'm pretty much on step 1 of step 1000 in terms of getting where I need to be to graduate. I've got both elementary and college algebra, trigonometry, pre-calculus, and calculus to learn/re-learn before I can even start taking your basic chemistry class. This, in conjunction with other bad decisions I've made in life, is going to cost me dearly in terms of time it takes to graduate. It's actually rather depressing, but there's nothing I can do about it at this point. Right now, all I'm doing is pretty much practicing as much as possible.
  13. Apr 18, 2014 #12


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    This is not possible all the time, and I will also argue that without understanding the mathematics, you are only understanding physics at a very superficial level! So you can't even appreciate it "first"!

    I've written elsewhere on why a lot of people find quantum mechanics to be so difficult, and I presented the argument on why it is probably due to their lack of understanding of the mathematics. Despite what you have said, I do not believe you know what QM is. You only know the EFFECTS of QM, but not its true ideas and description, which can only be understood via mathematics, which is not in dispute.

    But more importantly, without mathematics, what you will see are these various disjointed ideas and phenomena, without any realization that they are either the manifestation of the same thing, or that these have similarities. Would you be able to realize that the same phenomenon that causes the celestial bodies to orbit a system is also responsible for an apple falling to the ground? Would you realize that the same description of the interaction of quasiparticles in a superconductor actually is a mathematical equivalent of the Higgs mechanism?

    These were NOT realized simply by understanding physics intuitively, but being able to actually understand the mathematical description of it! You only get a superficial glimpse of physics without the mathematics. Period!

    Coming back to the OP's question: You need to know Algebra, Geometry, Trigonometry (which should come with Geometry), and Intro Calculus to be able to do calculus-based intro Physics.

  14. Apr 18, 2014 #13
    Here is the lower division math sequence at Pierce college:
    -Elementary Algebra
    -Plane Geometry/Intermediate Algebra
    -Calculus 1
    -Calculus 2
    -Calculus 3/Linear Algebra
    -Differential Equations

    The early classes are offered summer/winter (the first year I attended they offered up to calculus 2 in the summer, but have since ceased doing so, although some schools still do). So assuming you start out in prealgebra, it would be possible to be in trigonometry by the start of the next year. I was placed into trigonometry when I started school, although all the classes were full in fall so I didn't get to take it until spring. After that I took precalculus in the summer, calculus 1 in the fall, and calculus 2 in the spring and then transferred to UCLA where I took calculus 3A, linear algebra, and differential equations fall followed by calculus 3B winter. I will be graduating this June after a total of two years at community college and two at UCLA (so four altogether). So with an extra year tacked on for the early math classes, it would still be perfectly possible to graduate in five years total (plus you can self study and get all your GE out of the way while you are taking the earlier math).

    Math goes by quickly in college. A year's worth of high school math can be completed in as little as eight weeks in college, so even if you start out in prealgebra, time-wise, you probably aren't as behind as you think. Just start at community college (which is a lot cheaper than a university), work hard, and be patient; you will get to where you want to be soon enough.
  15. Apr 18, 2014 #14
    I'm already in a university, but I've primarily taken Gen-Ed courses. I agree that I should probably go to a community college, and then transfer, but I'm already here now. It's not that great of a school, but at least the tuition isn't ridiculous like it is in some colleges. It's really only going to take me forever to graduate if I can't afford to take classes over the summer.
  16. Apr 18, 2014 #15
    I think most universities will let you do summer courses at community college, so you can do the lower division math there. You can also probably do winter at community college if your school is on the semester system.
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