Q3: Find the greatest common divisor of 159 and 45.Ī3: GCD(159, 45) = 3. Q2: Is 17 a prime number? Why or why not?Ī2: Yes - 17 is only divisible by itself or 1, making it a prime. Q1: Is 16 a prime number? Why or why not?Ī1: No - 16 can be divided by 4, making it not a prime (primes are only divisible by themselves or 1). This list is in no way exhaustive, and we highly recommend consulting additional sources such as a maths teacher or lecturer while preparing for a test or exam. We've compiled a few short practice problems below. The best way to improve your understanding of number theory (in terms of math study tips) is through consistently answering practice problems.Īctive problem solving engages areas of the mind that are not engaged while passively reading, and allows you to ‘work out' the conceptual frameworks that underlie your understanding. If you like numbers, you're definitely in the right class. Many algorithms have been created to verify prime-ness with high computational efficiency, and proponents of number theory use these algorithms to help create novel encryption schemes, search for patterns in prime numbers, and use integers to study other types of numbers (rationals, reals, etc).Īt its core, though, number theory is foundationally abstract and is really the study of numbers for the sake of studying numbers. One of the foundational theories in number theory is the Foundational Theorem of Arithmetic, which shows that every positive integer greater than one can be written as the product of primes. The reason prime numbers are so important is because they are the core features that mathematicians use to work with novel mathematical constructs prime numbers share characteristics across their set, and these characteristics help inform us about the nature of new numbers.Ĭommon questions that number theory deals with are things like ‘is this a prime number?' or ‘what's the best way to generate massive prime numbers?'. The basic, underlying concepts behind number theory are integral to understanding more advanced subjects like algebra, calculus, encryption, computer science, and more.Īt its core, number theory deals with integers (1, 2, 3) and their negatives (-1, -2, -3), and how they relate to prime numbers, numbers that are only divisible by themselves and the number one. Number theory has long been called the Queen of Mathematics, for the simple reason that ‘every other mathematical subject must first listen to her'. In this guide, we give you a brief, effective set of math study tips to introduce you to number theory and help you maximize your ability to solve problems. It's also often difficult to wrap your head around the purely abstract nature of many of the lemmas and corollary's present in your average number theory textbook, which can make scoring well in a number theory class highly difficult.īut like most difficult things, it's not impossible.ĭoing well in number theory mostly depends on your ability to understand a few basic concepts, and then extrapolating from there. Many students trip up on proofing and on expressing the correct answer succinctly. Number theory is foundational to a strong understanding of advanced mathematics, but that's not to say it's easy to learn.
Math Study Tips: Introduction to Number Theory