Combinatorics is a branch of mathematics concerning the study of finite or countable discrete structures. Aspects of combinatorics include counting the structures of a given kind and size deciding. Combinatorial problems arise in many areas of pure mathematics, notably in algebra, probability theory, topology, and geometry, and combinatorics also has many applications in optimization, computer science, ergodic theory and statistical physics. Many combinatorial questions have historically been considered in isolation, giving an ad hoc solution to a problem arising in some mathematical context. In the later twentieth century however powerful and general theoretical methods were developed, making combinatorics into an independent branch of mathematics in its own right. One of the oldest and most accessible parts of combinatorics is graph theory, which also has numerous natural connections to other areas. Combinatorics is used frequently in computer science to obtain formulas and estimates in the analysis of algorithms. Number theory is the branch of pure mathematics concerned with the properties of numbers in general, and integers in particular, as well as the wider classes of problems that arise from their study. In elementary number theory, study integers without use of techniques from other mathematical fields. Questions of divisibility, use of the Euclidean algorithm to compute greatest common divisors, integer factorizations into prime numbers, investigation of perfect numbers and congruences belong here. Several important discoveries of this field are Fermat's little theorem, Euler's theorem, the Chinese remainder theorem and the law of quadratic reciprocity. The properties of multiplicative functions such as the Möbius function and Euler's φ function, integer sequences, factorials, and Fibonacci numbers all also fall into this area.

Actors' guild

Every actor should strive to become a member of one or all of these guilds; it's a step toward a professional career. Go to acting guilds to get more information on the criteria for each. The most reputable unions for acting are SAG (Screen Actors Guild), AFTRA (American Federation of Television and Radio Artists) and AEA (Actors' Equity Association), which represents actors and stage managers in theatre. Each of these unions have specific regulations for becoming a member. A guild is an association of people of the same trade or pursuits (with a similar skill craft), formed to protect mutual interests and maintain standards of morality or conduct.

To improve as an actor, acting lessons are an important tool. Visit lessons to find out what training would be best for you. They involve one or more students (also called pupils) being taught by a teacher or instructor. Acting lessons may be either one section of a textbook (which, apart from the printed page, can also include multimedia) or, more frequently, a short period of time during which students are taught about a particular subject. Acting lessons may consist of exercises, cold readings or on-camera commercial techniques.

How to audition

Auditions are a nerve-wracking and a difficult experience for most actors, but they are an essential part of the job. If you are called for an audition, you will often receive "sides", which are simply a few pages of the script that you will be expected to read. The most you can do is prepare the best you can and go into the audition confident; not arrogant, confident. Auditioning is a skill and the more you attend, the better you will become. Just stick with and be yourself; you should do fine. To learn more about the audition process, go to the audition process. How to audition is a basic overview of the audition process.

Do people always say you should do something with that great voice of yours? Do you listen to the voices on TV and radio and think: That sounds like fun. I'd like to do that! What talent should do is make themselves "stick out" at an audition. Be on time, prepared and have several different voices for each character. Versatility and the ability to take direction are the key ingredients! Voice over work can be extremely lucrative and many actors make a living solely from voice over work. If you would like to get into the voice over business, but aren't sure how to get a demo or find a reputable company, go to Voice Over Work.