Logic is the formal mathematical study of the methods, structure, and validity of mathematical deduction and proof. The mathematics of modern computer science is built almost entirely on discrete math, in particular combinatorics and graph theory.
This means that in order to learn the fundamental algorithms used by computer programmers, students will need a solid background in these subjects. Course Introduction Discrete mathematics describes processes that consist of a sequence of individual steps, as compared to forms of mathematics that describe processes that change in a continuous manner.
The major topics we cover in this course are single-membership sets, mathematical logic, induction, and proofs. Discrete mathematics is the study of mathematics confined to the set of integers. While the applications of fields of continuous mathematics such as calculus and algebra are obvious to many, the applications of discrete mathematics may at first be obscure. Discrete Mathematics is a rigorous fourth-year launch course that differs from the courses that precede it in that the mathematics is focused in discrete topics instead of continuous functions.
In this course, reasoning and modeling are primary drivers of instruction. Pascal's Triangle :. Pascal's triangle is a triangular array of binomial coefficients that can visually illustrate several of their properties. Permutation :. In combinatorics, a permutation is a rearrangement of the elements in an ordered list S into a one-to-one correspondence with S itself. Combinatorics studies the number of possible ways of doing this under various conditions.
Recurrence Relation :. A recurrence relation is a mathematical relationship expressing the members of a sequence as some combination of their predecessors. Chromatic Number :. The chromatic number is the smallest number of colors necessary to color the vertices of a graph or the regions of a surface such that no two adjacent vertices or regions are the same color. Complete Graph :. Connected Graph :. Cycle Graph :. Directed Graph :. A directed graph is a network in which each edge is specified as going in a particular direction.
Graph :. In graph theory, a graph, also called a network, is a collection of points together with lines that connect some subset of the points. The set of objects studied in discrete mathematics can be finite or infinite. In real-world applications, the set of objects of interest are mainly finite, the study of which is often called finite mathematics. Di sc rete mat h plays the significant role in big data analytics. The Big Data era poses a critically difficult challenge and striking development opportunities: how to efficiently turn massively large data into valuable information and meaningful knowledge.
Discrete mathematics produces a significant collection of powerful methods, including mathematical tools for understanding and managing very high-dimensional data, inference systems for drawing sound conclusions from large and noisy data sets, and algorithms for scaling computations up to very large sizes. Discrete mathematics is the mathematical language of data science, and as such, its importance has increased dramatically in recent decades.
IN SUMMARY, discrete mathematics is an exciting and appropriate vehicle for working toward and achieving the goal of educating informed citizens who are better able to function in our increasingly technological society; have better reasoning power and problem-solving skills; are aware of the importance of mathematics in our society; and are prepared for future careers which will require new and more sophisticated analytical and technical tools.
It is an excellent tool for improving reasoning and problem-solving abilities. We highly suggest that starting from the 6th grade, students should some effort into studying fundamental discrete math, especially combinatorics, graph theory, discrete geometry, number theory, and discrete probability.
Students, even possessing very little knowledge and skills in elementary arithmetic and algebra, can join our competitive mathematics classes to begin learning and studying discrete mathematics.
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