Adding to Nava’s post, I always find it interesting - and slightly disconcerting - that a lot of school systems present algebra, trigonometry and geometry as separate topics, as if anything useful can be done in one without knowing at least a little of the others. In my school system, I had Math classes, which covered everything in intertwined courses that covered a full year (my high school didn’t have a semester set up).
Saying that you don’t need to know geometry might be true in the sense that a lot of what you might have learned in a high school Geometry class isn’t used, but of course you will need to be able to recognize the formulas for areas and volumes of circles and spheres and be able to work with similar triangles and understand how to find a given angle given other information. Some word problems won’t give you the equations - you’ll have to figure them out themselves for things like deriving the volume of a bowl (a half sphere) and such. There’s not much point to trying to solve any Calculus problems if they have no relation to the physical world, and topics related to geometry and trigonometry are the means to do that.
I second the idea that you obtain a good pre-calculus textbook; looking at one now will tell you what sorts of topics you need to understand and help you narrow your focus on topics from the Khan Academy while building up the skills you need for calculus. It should be rather easy to find out what textbook your school is using in the Cal I, II courses and it might help you to get the pre-cal book by the same author. On the other hand, a different author might help reinforce a topic if he or she presents the material slightly differently.
I think it only came up in higher level calculus classes for me (or Ordinary/Partial differential equations classes) but an understanding of the basics of linear algebra came in handy - especially doing a simple elimination to solve a 3x3 system. It wasn’t explicitly asked of me sometimes, but I’d occasionally be given problems where you end up with three solutions that need to be solved. Most students just start substituting equations/using general algebra to solve them at this point, but I tended to go the matrix route because it was much faster. It won’t really be required for that you intend to study, but since you’re in the computing/gaming fields it might prove to be really useful for you later on (or, you might find you’ve already seen this stuff in your programming courses!)
Good luck!
FWIW, I went back to school at 26 years old and relearned my math from Cal I through to the end of an engineering degree. You can learn anything, if you make the effort.
A lot depends on how the class is taught, and how you learn.
For me personally, I found calculus very easy to learn, but I often had to relate what we were doing to its geometric equivalent (i.e. an integral is just the area under a curve and the derivative is the slope of the curve). Some classes teach calculus with a bunch of proofs and theorems and lots and lots and lots of equations. That to me was a bit meaningless, but there are a lot of math weenies who enjoy that sort of thing and learn from it. If you “dread math” (as stated in the OP) you’re probably not the math weenie type, and relating what you are doing to its practical geometric use may be helpful in allowing you to understand it.
This makes me think that you will likely need to focus on geometry. You’ll also need to have a solid background in algebra just to be able to manipulate the equations around. If you take this approach, the proof type stuff you do in trig isn’t so important, and the only bits you’ll probably really need out of trig are things like the sin/cos/tan relationships and that sort of thing.
I’ve always had an easy time with math, but the key for me is to understand the purpose behind what I’m doing. Once I understand the “what” and “why”, the “how” part becomes much easier. Learn why you are going what you are doing and it all will make more sense and will be much easier to remember (or at least it was for me).
This is a very good list.
A few other things I would add to the list is an understanding of how to combine 2 functions: f(g(x)). And an understanding of the laws of logarithms and exponents
The most important things that I think the OP might be lacking is a implicit understanding of how functions work. This is crucial for getting through calculus.
That pre-calc book he suggests is by Larson and Hostetler. I used various editions of their books in some of my Calc classes. I thought their texts were particularly good.
True, math hasn’t changed all that much in decades. But the textbooks have, I think. As I wrote earlier, I think they are getting steadily more dumbed down. So that’s another reason to hit up the used-book stores looking for older books, besides them being cheaper. The college textbook industry is a major racket, and everybody knows it.
That’s how it works in Spain as well, we didn’t start getting courses labeled after specific branches of Math until college. Previously, each year would focus on whatever aspects the national curriculum asked for, but the first couple of “themes” were always “review of [whatever was studied in previous years that is required in order to understand what comes next]”.
For example, my 10th-grade Math involved trig, limits, series and derivatives, each building both from the material of previous years and from what had already been seen that year. Sometimes the curriculum would step back for a bit; for example, we’d done limits, then we’d do a new type of series, then we’d see how to do limits for that new type of series.
Yes! Good catch, Buck Godot! This combination of functions f(g(x)) is called composition and it comes in BIG in Calculus. And typically doesn’t get much emphasis in Algebra, although it may be briefly mentioned. When you first see it in Algebra, be sure to get it engraved into your engrams! When I took Calc I, everybody (myself included) had a bear of a time with this for a while until we got it down.
First off, Relunctant Mathematics, don’t be intimidated. Calc is among the easiest math courses I ever took. I had the advantage of good teachers. Fortunately, it’s one of the easier ones to teach yourself as well. I’m not sure how your school handles it, but I too went back to school after having no math in years. I got through with flying colors.
Calc is extremely logical. They may include some miscellaneous material under that heading, which isn’t exactly Calc but related to interpreting what you find in it. That’s why you might need some basic geometry. You could use it to compare two graphed functions, for instance.
But for a simpler method - just ask your school. Quite often, they can give you a rundown of basic needs and even give you a quick math test to show where you need work. I did this on the first day of class, got crushed, and still got an A+ by the time the first test rolled around. (Make sure you ask about natural log functions and a rundown of what various power notations mean.)
Complete tripe. I can personally vouch that it’s not true, for several reasons. First, schools tend to give everyone the same instruction, regardless of personal need. Often enough, somebody won’t get it at first. Given time, they practice with other things and the old difficult problem becomes trivial. Second, people may find a new apporoach they understand better. Third, they somtimes just need to digest the math a while. Courses might be taught at breakneck speed, jumping from one thing to the next; some people seem to suddenly improve their math skills weeks or months after first seeing (and failing) a problem.
My credentials in math education are flimsy to put it mildly, but let me opinionate anyway if only to stand correction. Is there not an Analysis I for Math Majors completely different from the Calculus I for Engineers and Technicians? Which such course we’re preparing for makes a big difference. Either way, I doubt specialized knowledge in either geometry or trig would be of great importance, excepting simple formulae for area, angle, etc. As a mandatory prerequisite perhaps Alg I and, for practice, at least two or so of {Alg II, Geom, Trig}.
The comment about epsilon/delta doesn’t sway me. From simple algebra, one can learn to express epsilon as a function of x and delta; ability to do this will stand one in good stead, e.g. should a formula be otherwise forgotten, or the intricacies of a calculus proof otherwise confound.
Yes, but it is normally at least a junior-level course, and two or three semesters of calculus is usually a prerequisite. Analysis is basically calculus redone in a very rigorous manner, with the emphasis on proofs, rather than calculation.
In my humble opinion: algebra, algebra, algebra. Everything else you can pick up on the way, as suits your needs. (But, one must note, much depends on the nature of the course you will be taking and your goals in taking it…)
Is there not an Analysis I for Math Majors completely different from the Calculus I for Engineers and Technicians? Which such course we’re preparing for makes a big difference. Either way, I doubt specialized knowledge in either geometry or trig would be of great importance, excepting simple formulae for area, angle, etc. As a mandatory prerequisite perhaps Alg I and, for practice, at least two or so of {Alg II, Geom, Trig}.