I want to learn more math, where do I go from here?

Question

I am a sophomore at university. Unfortunately, because of the pre-requisite system, I am in PreCalculus. I have already completed a calculus course in high school, and have completed 2 semesters of "Calculus for Business & Life Sciences" at university. I am familiar with all basic math up to calculus. I wish to learn more math, and to become as knowledgeable as possible about the more advanced topics in mathematics. I am not able to join the advanced classes now, so I would like to learn on my own. Please recommend some books and topics for me, I would like to start with material that is covered after Calculus I. Any information is helpful.

Answer 1

Some books I enjoyed very much in my youth are
Mathematics in Everyday Things and
One Two Three Infinity.
Another good way to learn more math is to take the course in discreet math or finite math that is offered at just about every university. This is a required course for liberal arts majors and social science majors, and it is greatly underappreciated. It is usually taught at the sophomore level so it would be within your range.
Actually, it is a survey course of advanced math topics that one would study in depth as a math major, at the graduate level. If you take this course, you'd get exposed to all sorts of advanced topics, enough to whet your interest to study these further on your own. You'd be introduced to combinatorics, number theory, set theory, boolean algebra, formal logic, statistics, etc. And the professor would appreciate having a student who is truly interested in the math.

Answer 2

What sort of calculus have you learned? If you have learned differential calculus (taking derivatives), you can still learn about the flip side of the same coin, integral calculus. As you know, when you differentiate a function, the new function you obtain describes the slope of the original function. Well, if you apply mathematically opposite changes to the original function, you obtain an integral function which describes the area contained by the original function. Since integration and differentiation are mathematically opposite, their effects (nearly) cancel out, so (within certain limits) the integral of a differential function is the original function, and vice versa.

Once you understand differential and integral calculus, I would recommend some linear algebra using matrices. Another person mentioned parametric equations, which are very neat (and which I don't understand myself).

If you're a visual kind of thinker, you may wish to teach yourself about POV-Ray. It's a free, open source raytracing 3D program. Using an object called an isosurface, it can display three-dimensional functions very realistically. I use the unofficial MegaPOV version, which is also free and has more features. POV-Ray runs well on any modern computer.

Answer 3

L O L 9/10 x

Answer 4

By calc, I presume differential and integral calculus.

*Partial differential equations is a logical step up from what you've already had.

*Complex variables math, where you learn about imaginary numbers, is also useful.

*And so-called linear algebra can be used in a variety of professional domains.

*Last, but not least, vectors analysis and curvinlinear coordinates are employed by both the hard and soft sciences.

Probability and statistics, and the design and analysis of experiments, are excellent higher level courses for someone going into an MBA or MS. You might slip these courses anywhere into the list above.

PS: Ooops almost forgot matrix algebra; very important for solving multiple equations with multiple variable...sometimes taught with linear algrebra, but could be a separate course.

Answer 5

A few other college-level topics outside of general calculus that come to mind:

- Linear Algebra. Certainly not to be confused with College Algebra or high school-level algebra. This deals with studying and solving linear equations, which have applications in almost every other subject out there. Linear Programming also follows from Linear Algebra
- Statistics/Probability. This spans all different levels of complexity.
- Differential equations. One of the great applications of calculus.
- Discrete Math. Related topics include combinatorics, graph theory and stochastic modeling.
- Numerical Analysis. Usually involves algorithms used to approximate calculations that can't be readily sovled.
- Number Theory. The study of numbers themselves (prime numbers, transcendental numbers, plus sets and subsets, etc.)

As for books, you can find hundreds of books on each of these subjects. It might be cheapest to find somebody on campus who's already taken some courses and wants to sell the textbook. Another great general math source I like is the website mathworld.wolfram.com.

I majored in math myself, and even then I realized there were classes I wanted to take that I couldn't fit in to my schedule or weren't specifically related to my concentration. But one of the professors reminded me this is typical, and that when you get up to a certain level and want to learn more math, you pretty much have to look for it on your own. So even with a full math schedule, you can't get classes on everything! There's a lot out there, though. Good look with your studies.

Answer 6

I assume you are a business or science major because PreCalculus and "Calculus for Business & Life Sciences" is for people who need remedial math skills.

Try talking to your guidance counselor and taking Calculus II, Calculus iii and Calculus IV.
Come back after you have completed these three and tell us you want to be challenged.
..

Answer 7

Heh heh I dunno where to go professionally but just for fun alphanumerically speaking system programming might jar your logic of usings the numbers to solve the numbers, base 16 is fun but nothing for getting to the basics like interrelating it at a glance with base 2.

There's a whole other worlds out there in fractals.

You can add columns of 3 digits from the right but can you do it from the left sure the square of fifty is 2500 hundred as sure as 4901 is the square of 49 being that 49 plus 50 = 99 and 99 is 100 from 5000 plus one just as the square of 48 is 48 plus 49 minus from 4901 is 4804 or 4 times 49 less than 2500 .

numbers are are the truest fun, they mostly don't lie or seldom change their perspective play with them to discover practical trueths and uses for them read structure and

take your favorite number between 0 and ten mulitply it by 12345679
then multiply that by 9

You can email mail me if you can tell me all about your answer i'd be curious lol

Ob1

Answer 8

typical topics after basic calculus include calc 2 and calc 3 (more advanced, including summations, 3 dimensional objects, double and triple integrals, etc.), differential equations, linear algebra, then followed partial differential equations, complex variables, etc. You can look into any of these topics, but there isnt a very specific order.

Answer 9

read popular articles on math to motivate you. math is not all calculus.

There are linear programming, matrices, discrete math, cryptography, numerical analysis, chaos theory, graph theory, projective geometry, dynamics, fluid dynamics, artificial intelligence etc. It is a very wide field and it all depends on your interest

Answer 10

did u try to join math club or something like that at ur college? get good books from book store...