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His interests include discrete mathematics and the history of mathematics. He is the author of several textbooks. He is the author of several textbooks. Johnsonbaugh earned a bachelor's degree in mathematics from Yale University , and then moved to the University of Oregon for graduate study. [ 2 ]
Discrete mathematics is the study of mathematical structures that can be considered "discrete" (in a way analogous to discrete variables, having a bijection with the set of natural numbers) rather than "continuous" (analogously to continuous functions).
Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous.In contrast to real numbers that have the property of varying "smoothly", the objects studied in discrete mathematics – such as integers, graphs, and statements in logic [1] – do not vary smoothly in this way, but have distinct, separated values. [2]
This book was an accumulation of Discrete Mathematics, first edition, textbook published in 1985 which dealt with calculations involving a finite number of steps rather than limiting processes. The second edition added nine new introductory chapters; Fundamental language of mathematicians, statements and proofs , the logical framework, sets and ...
Kawasaki's theorem (mathematics of paper folding) Kelvin's circulation theorem ; Kempf–Ness theorem (algebraic geometry) Kepler conjecture (discrete geometry) Kharitonov's theorem (control theory) Khinchin's theorem (probability) Killing–Hopf theorem (Riemannian geometry) Kinoshita–Lee–Nauenberg theorem (quantum field theory)
Discrete mathematics, also called finite mathematics, is the study of mathematical structures that are fundamentally discrete, in the sense of not supporting or requiring the notion of continuity. Most, if not all, of the objects studied in finite mathematics are countable sets , such as integers , finite graphs , and formal languages .
The four color theorem and optimal sphere packing were two major problems of discrete mathematics solved in the second half of the 20th century. [44] The P versus NP problem, which remains open to this day, is also important for discrete mathematics, since its solution would potentially impact a large number of computationally difficult ...
Baudhayana (8th century BCE) Believed to have been written around the 8th century BCE, this is one of the oldest mathematical texts. It laid the foundations of Indian mathematics and was influential in South Asia. It was primarily a geometrical text and also contained some important developments, including the list of Pythagorean triples ...