General Mathematics: Revision and Practice

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Combinatorics, the art of enumerating mathematical objects that satisfy some given constraints. Originally, these objects were elements or subsets of a given set; this has been extended to various objects, which establishes a strong link between combinatorics and other parts of discrete mathematics. For example, discrete geometry includes counting configurations of geometric shapes The book can still use some organization of topics. Presenting the topics in modular form will be more beneficial to students and other users of the book. Discrete mathematics, broadly speaking, is the study of individual, countable mathematical objects. An example is the set of all integers. [48] Because the objects of study here are discrete, the methods of calculus and mathematical analysis do not directly apply. [c] Algorithms—especially their implementation and computational complexity—play a major role in discrete mathematics. [49]

a b c Straume, Eldar (September 2014). "A Survey of the Development of Geometry up to 1870". ePrint. arXiv: 1409.1140. Bibcode: 2014arXiv1409.1140S. Goldman, Jay (1997). The Queen of Mathematics: A Historically Motivated Guide to Number Theory. CRC Press. pp.1–3. ISBN 978-1-4398-6462-3 . Retrieved November 11, 2022. The book can be divided in different modules so that it is not overwhelming to leaners. This way students can work at their own pace and print materials that they need more focus on. Presenting materials by chunks is more discernible,Projective geometry, introduced in the 16th century by Girard Desargues, extends Euclidean geometry by adding points at infinity at which parallel lines intersect. This simplifies many aspects of classical geometry by unifying the treatments for intersecting and parallel lines. Perisho, Margaret W. (Spring 1965). "The Etymology of Mathematical Terms". Pi Mu Epsilon Journal. 4 (2): 62–66. JSTOR 24338341. Wise, David. "Eudoxus' Influence on Euclid's Elements with a close look at The Method of Exhaustion". jwilson.coe.uga.edu. Archived from the original on June 1, 2019 . Retrieved October 26, 2019.

In the 6th century BC, Greek mathematics began to emerge as a distinct discipline and some Ancient Greeks such as the Pythagoreans appeared to have considered it a subject in its own right. [76] Around 300 BC, Euclid organized mathematical knowledge by way of postulates and first principles, which evolved into the axiomatic method that is used in mathematics today, consisting of definition, axiom, theorem, and proof. [77] His book, Elements, is widely considered the most successful and influential textbook of all time. [78] The greatest mathematician of antiquity is often held to be Archimedes ( c. 287– c. 212 BC) of Syracuse. [79] He developed formulas for calculating the surface area and volume of solids of revolution and used the method of exhaustion to calculate the area under the arc of a parabola with the summation of an infinite series, in a manner not too dissimilar from modern calculus. [80] Other notable achievements of Greek mathematics are conic sections ( Apollonius of Perga, 3rd century BC), [81] trigonometry ( Hipparchus of Nicaea, 2nd century BC), [82] and the beginnings of algebra (Diophantus, 3rd century AD). [83] The numerals used in the Bakhshali manuscript, dated between the 2nd century BC and the 2nd century AD a b c d e f Kleiner, Israel (December 1991). "Rigor and Proof in Mathematics: A Historical Perspective". Mathematics Magazine. Taylor & Francis, Ltd. 64 (5): 291–314. doi: 10.1080/0025570X.1991.11977625. JSTOR 2690647.The book is well organized, arranging the skills in a logical manner that enables the student to be ready for each new concept. The history of mathematics is an ever-growing series of abstractions. Evolutionarily speaking, the first abstraction to ever be discovered, one shared by many animals, [71] was probably that of numbers: the realization that, for example, a collection of two apples and a collection of two oranges (say) have something in common, namely that there are two of them. As evidenced by tallies found on bone, in addition to recognizing how to count physical objects, prehistoric peoples may have also known how to count abstract quantities, like time—days, seasons, or years. [72] [73] The Babylonian mathematical tablet Plimpton 322, dated to 1800BC