I've been interested in math and physics sence middleschool. However, I have never pursued a higher education in the matter, other then what I have taught myself. I would like to go to college soon, but in the mean time was wondering on ways that I could get myself prepared. Ive done some reading around here and it's becoming pretty clear that I need to work more on my math. I have never been able to teach myself very mathematics very well from studying books. Insted, I have acceled when taught in some verbal way. My question is this; Are their any ways I might be able to improve my ablitly to teach myself math from a textbook, and, what level of math/physics knowledge should I intend upon acheiving prior to or even during college.
khan academy has videos and exercises for most of high school math. And he has videos but unfortunately no exercises for college math calc 1-diff eq/linear algebra edit: MIT open courseware too
there is always the option of recording notes also audio lectures you can download. Is it that you can only learn auditory or maybe that you aren't revising the maths efficiently. Maths is not like literature of law you can't just read and make notes, one must work through the problems or examples and if necessary over and over again until you can do it without the aid of the book
Khan Academy and MIT's OCW are great for learning the techniques to solve math problems. However, to actually become good at math, IMO, you need to practise, practise and more practise. The more hours you spend, the better you'll get.
Completely right with maths its all about the practice its like learning a hand trade like drawing for some the more you practice the more you will understand it
If you do plan on going back to college, you should definitely take the advice above (Khan Academy is great for pre-calculus topics). Figure out what level of mathematics you are comfortable with, then find the syllabus of the course at a university online. Learn the topics in the order the syllabus dictates, and find some source of problems to practice with. Practice really is the key to mathematics. It sounds silly because often you can understand a concept very easily, but you won't be comfortable with it, or excel at it without (sometimes boring) practice. You should be able to learn up to Calculus I without any trouble. Then you could place into Calculus your first semester. Considering, the alternative is to take, Trigonometry, Precalculus, Algebra, and perhaps 2 more courses of Intermediate/Pre-algebra, this can really save you some money and speed up your study. Really practice at it though. Much of the difficulty that comes from higher level undergraduate mathematics (in my experience so far) seems to stem from the rigor of algebra.
Ok thanks. As to your question. My more specific problem is the interpretation of the math as expressed by the character of the said book. I can never seem to understand 'why' this works, and what it pertains to in real life. Thank you for your advise!
If you need to start from Algebra I or II and you need textbooks, I would recommend the books by Margaret Lial: Introductory Algebra Intermediate Algebra These are college textbooks for remedial classes. These books could be considered self-teaching texts, because there are a lot of examples that are explained. There are also a lot of exercises. The same author also has books in College Algebra and Trigonometry (aka Precalculus), but I have not looked at those.
I see what you mean i think that is probably about finding the right book, a lot of them are very drone like, maybe the key is to find some extracts from different books and see which ones feel most comfortable
Hey thanks for the input. I'm already finding this helpful. I need to start thinking about buying some specific books, as well as other alt. I'm just wondering, is this khan academy a website? I'm a little confused, as I dont get out much. :D
from what i have just seen by googling it lol its got loads of resources videos on subjects and exercises i won't put the link up cause i don't think its allowed but google it and take a look. I wouldn't worry i rarely get out
Can't you take evening classes somewhere? I'm in the UK and would recommend people take evening classes at the local technical college. Surely other countries have something equivalent?
The best way to improve your maths skills are; 1. practice 2. develop a deeper understanding Both can be obtained through using textbooks correctly (that means taking notes throught the book and doing all the problems) In terms of what you should know before you go to college/uni.. I wouldn't say there is a limit to how much you should know, the more you know the easier your math classes will be (which will be a blessing since I've heard a LOT of stories about maths being very poorly taught) and if you keep up your rate of learning you'll constantly be ahead! I use to think that I wasn't good at learning from textbooks either. It turned out I just wasn't using textbooks correctly and that I was hand waving past the problems. Learning from textbooks is an aquired skill, yes, but it is perfectly achievable and it's a very useful skill to have. It was either that or I had some very poorly written textbooks. Take your textbook, read a section, take notes on that section (irl notes on a piece of paper with a pen), read the notes at the end of each section and make sure you understand them. Continue onto the next section and repeat until you land at the problems. Attempt every problem, spend as much time as you need to completely every last one before moving onto the next chapter. Repeat until you have finished the book. Another set of things you should learn are derivations, learn how things are derived, don't just go straight for remembering formulas for things, learn how they got there, learn to do them without having to look at notes, you can think of these derivations as the forms you learn if you've ever done a martial art :p I'll give you the list of books and material I've used in my first year of learning maths (after you've gone through everything you should know exactly where to go to continue your journey) 1)Introduction to Linear Algebra - G. Strang (alongside the mit ocw course also by gilbert strang) an introduction to linear algebra, matrices have never been so pretty 2)Mathematical Methods in the Physical Sciences - M Baos a good all round welcome to a lot of neat things, integral transformations, differential equations, orthogonal functions, the works 3)How to prove it - A Structured Approach - Daniel J. Velleman this is the single best 'intro to writing/reading proofs' book I have ever seen 4)Differential Forms - A Compliment to Vector Calculus - S. Weintraub differential forms are pretty handy, the goal of the book is to prove stokes theorem 5)Introduction to Tensor Calculus and Continuum Mechanics - J. H. Heinbockel (this one is free online) this is the single best book on tensors I have ever seen.. seriously.. you actually get to understand what tensors are and what they do 6)Baby Rudin aka Principles of Mathematical Analysis - Walter Rudin introduction to real analysis (this is why you read how to prove it ) 7)Modern Algebra with Applications - Gilbert Nicholson a nice little coverage of modern algebra, fields, rings, quotient groups, they're all here 8)Advanced Linear Algebra - Steven Roman don't be scared by the fact it says graduate texts in mathematics, you'll be able to understand it from what you know by now Good luck!
Khanacademy.org is a fantastic resource to teach yourself elementary mathematics. The URL is: http://www.khanacademy.org/ Enjoy ;D
and my favorite book for the wandering future mathematician: http://www.amazon.com/Mathematics-1...7192/ref=sr_1_1?ie=UTF8&qid=1325786989&sr=8-1
Hi, You might find "How to Solve It" by George Polya helpful to pick up some ideas on how to go about working on problems. The one step he probably misses out is not not having "Don't Panic!" written in big friendly reassuring letters in his list like the cover of the Hitchhikers guide to the galaxy. When trying to work out how fundamental things work, try and turn them into real physical experiments with "things." (For a lot of number related problem, Lego bricks or similar are really good since you can get different coloured ones which often helps make patterns stand out.) Start by plugging numbers in and manipulating your "things" until you can "see" how the things work. Then try and see how the generalisation "falls out" of your specific examples. Also, try and link the things you are learning to other areas of mathematics - for example you can often think of geometric interpretation of a lot of things. If you can find it you might also find: * "Learning and Doing Mathematics" by John Mason (I have the 2nd edition), * "Thinking Mathematically" by J. Mason, L. Burton and K. Stacey (I have the 1st and 2nd editions) Useful. I think Thinking Mathematically probably expands on the 1st but they complement Polya on how to go about tackling problems, what to do when you get stuck etc. Hope that helps, Windscale.