discrete math concepts

Mathematical induction is a type of proof that uses the same idea as a recursive set; it says if you can prove the first idea and then say that the second idea is implied by the first idea everything else falls into place. Fun lessons, multiple-choice quizzes and a practice exam are available to quickly improve your comprehension of symbolic logic, linear programs and more. A mathematical statement with an equals sign is an equation. For example we looked at the Euclidean Algorithm to solve Greatest Common Factor problems. Math itself is one big concept, and it’s chock full of so many smaller mathematical concepts that no one person can possibly understand them all — even with a good dose of studying. Pi is everywhere in math. One example is trigonometry, the study of triangles. . Chapter 3 15 / 28 . The basic problem was this one: All the fractions listed in the preceding sequence are between 0 and 1 on the number line. Functions: A function is a mathematical machine that takes in one number (called the input) and gives back exactly one other number (called the output). Required fields are marked *. If you need help understanding tautologies in math, the dominant strategy in game theory or logic laws, you've reached the right place. The xy-graph: Before the xy-graph (also called the Cartesian coordinate system) was invented, algebra and geometry were studied for centuries as two separate and unrelated areas of math. Automata theory and formal language theory are closely related to computability. Next we looked at algorithms. Teachers have found that discrete mathematics offers a way of motivating unmotivated students while challenging talented students at the same time. Creativity, at its best, will enable you to solve problems in discrete math as opposed to the rigid formulas in calculus and linear algebra. Mark Zegarelli is the author of many successful For Dummies titles on math, logic, and test prep topics. Discrete mathematics will make math concepts come alive for your students. The graph, invented by French philosopher and mathematician René Descartes, brought algebra and geometry together, enabling you to draw solutions to equations that include the variables x and y as points, lines, circles, and other geometric shapes on a graph. Creativity, at its best, will enable you to solve problems in discrete math as opposed to the rigid formulas in calculus and linear algebra. Discover what a tautology is, and learn how to determine if a statement is a tautology by constructing a truth table. The originators of the basic concepts of Discrete Mathematics, the mathematics of finite structures, were the Hindus, who knew the formulae for the number of permutations of a set of n elements, and for the number of subsets of cardinality k in a set of n elements already in the sixth century. Discrete Mathematics: Past, Present and Future, The originators of the basic concepts of Discrete Mathematics, the mathematics of finite structures, were the Hindus, who knew the formulae for the number of permutations of a set of, tight connection between Discrete Mathematics and Theoretical Computer Science. The concept of zero as a number arose independently in several different places. Here we took a basic look at the different ways to tell computers what to do, and how effective they are. Your email address will not be published. While many of the basic combinatorial results were obtained mainly by ingenuity and detailed reasoning, the modern theory has evolved into a much deeper theory with a systematic and powerful toolkit. Equals signs and equations: The humble equals sign (=) is so common in math that it goes virtually unnoticed. The fundamental nature of Discrete Mathematics, its tight connection to other disciplines, and its many fascinating open problems ensure that this field will continue to play an essential role in the general development of science. In this self-paced chapter is a comprehensive overview of basic concepts in mathematical logic and discrete math. Simply explore our entertaining online lessons. In the second unit we looked at sequences, sums, induction, algorithms, and number theory. After that, you have to go half the distance that still remains). The set of numbers or objects can be denoted by the braces {} symbol. I’m taking a test tomorrow, so I’m going to use this post to help me study. Discrete Mathematics, Study Discrete Mathematics Topics. Concepts and questions of Discrete Mathematics appear naturally in many branches of mathematics, and the area has found applications in other disciplines as well. However, such methods usually provide non-constructive proof techniques, and the conversion of these to algorithmic ones may well be one of the main future challenges of the area (involving cooperation with theoretical computer scientists). Discrete Mathematics Topics. Another interesting recent development is the increased appearance of computer-aided proofs in Combinatorics, starting with the proof of the Four Color Theorem. The real number line: Every point on the number line stands for a number. To me, this is what makes computers ‘smart’, the fact that they can distinguish one kind from another (maybe someday they’ll be able to tell good from bad, right from wrong). Beyond this, π is a transcendental number, which means that it’s never the value of x in a polynomial equation (the most basic type of algebraic equation). credit by exam that is accepted by over 1,500 colleges and universities. Using these rules we are able to find primes and come up with a division algorithm. But how can you have an infinite number of numbers in a finite space? And the Hindu-Arabic system used throughout most of the world today developed from an earlier Arabic system that used zero as a placeholder. Whateveryour conceptionofwhatmathematicsis,tryapplyingtheconceptof“discrete” to it, as defined above. Illustration of Big-O Notation f(x) = x2 + 2x + 1, g(x) = x2. To apply the concept of algorithms to my programming class an algorithm is like pseudocode. 8 Sets are essentially primitive databases, in fact, a csv file, that you can open in excel, is just a set of numbers or strings (csv stands for comma separated values). I’m almost done with the course so I can share some of the things I’ve learned and how (I think) they apply to Comp Sci. Anyone can earn credit-by-exam regardless of age or education level. As if it didn't take me long enough to learn how to spell rhythm, now I have to learn algorithm? Most of the new significant results obtained in the area are inevitably based on the knowledge of these well developed concepts and techniques, and while there is, of course, still a great deal room for pure ingenuity in Discrete Mathematics, much progress is obtained with the aid of our accumulated body of knowledge. Combinatorial topics such as Ramsey Theory, Combinatorial Set Theory, Matroid Theory, Extremal Graph Theory, Combinatorial Geometry and Discrepancy Theory are related to a large part of the mathematical and scientific world, and these topics have already found numerous applications in other fields. 10 Math Concepts You Can’t Ignore. My test is on the second unit so I'll have to go over some induction examples, and also memorize the formulas for recursive sequences and the rules of arithmetic. Discrete mathematics is the part of mathematics devoted to the study of discrete (as opposed to continuous) objects. LP models are then used to formulate some common types of decision problems, and examples are given. Math itself is one big concept, and it’s chock full of so many smaller mathematical concepts that no one person can possibly understand them all — even with a good dose of studying. Abusing notation, this is often written as f(x) = x2 + 2x + 1 is O(x2). Princeton, New Jersey Not sure what college you want to attend yet? Other chapters within the Indiana Core Assessments Mathematics: Test Prep & Study Guide course. It’s really important for computers to know whether something is the same or not. It's an excellent tool for improving reasoning and problem-solving skills, and is appropriate for students at all levels and of all abilities. Watch this video lesson and learn what truth values are and what a truth table looks like. There are two main ways of defining sequences, you can define the first term and have a rule from there (recursive), or you can define it abstractly (closed set). 08540 Some of these are simple but powerful concepts that (unfortunately) some viii. Combinatorial topics such as Ramsey Theory, Combinatorial Set Theory, Matroid Theory, Extremal Graph Theory, Combinatorial Geometry and Discrepancy Theory are related to a large part of the mathematical and scientific world, and these topics have already found numerous applications in other fields. Discrete Math Gives You An Added Advantage. The beginning of Combinatorics as we know it today started with the work of Pascal and De Moivre in the 17th century, and continued in the 18th century with the seminal ideas of Euler in Graph Theory, with his work on partitions and their enumeration, and with his interest in latin squares. How to convert spoken language into symbols is helpful, but to me the clearest application of logic to computer science is the use of truth tables. These old results are among the roots of the study of formal methods of enumeration, the development of configurations and designs, and the extensive work on Graph Theory in the last two centuries. Chapter 3 14 / 28. So does the symbol for infinity (∞). Saturday, December 17, 2011. Hybrid discrete and continuous mathematics, Discrete analogues of continuous mathematics. Notify me of follow-up comments by email. The tight connection between Discrete Mathematics and Theoretical Computer Science, and the rapid development of the latter in recent years, led to an increased interest in Combinatorial techniques and to an impressive development of the subject.

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