General Mathematics: Revision and Practice

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The text is extremely clear. All terms are defined precisely and in more detail than I have seen in any other math textbook. There are no assumptions that the reader already knows a piece of content, and every explanation is very clear and easy to understand. 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. I found the text consistent in its breakdown of objectives, attention to each and amount of practice for each chapter. Archaeological evidence shows that instruction in mathematics occurred as early as the second millennium BCE in ancient Babylonia. [168] Comparable evidence has been unearthed for scribal mathematics training in the ancient Near East and then for the Greco-Roman world starting around 300 BCE. [169] The oldest known mathematics textbook is the Rhind papyrus, dated from c. 1650 BCE in Egypt. [170] Due to a scarcity of books, mathematical teachings in ancient India were communicated using memorized oral tradition since the Vedic period ( c. 1500– c. 500 BCE). [171] In Imperial China during the Tang dynasty (618–907 CE), a mathematics curriculum was adopted for the civil service exam to join the state bureaucracy. [172]

a b Harper, Douglas. "mathematic (n.)". Online Etymology Dictionary. Archived from the original on March 7, 2013 . Retrieved November 26, 2022.All mathematical systems (for example, Euclidean geometry) are combinations of sets of axioms and of theorems that can be logically deduced from the axioms. Inquiries into the logical and philosophical basis of mathematics reduce to questions of whether the axioms of a given system ensure its completeness and its consistency. For full treatment of this aspect, see mathematics, foundations of.

Something becomes objective (as opposed to "subjective") as soon as we are convinced that it exists in the minds of others in the same form as it does in ours and that we can think about it and discuss it together. [154] Because the language of mathematics is so precise, it is ideally suited to defining concepts for which such a consensus exists. In my opinion, that is sufficient to provide us with a feeling of an objective existence, of a reality of mathematics ... The final version of the manuscript must by typeset using LaTex according to the Journal’s article style. The two subjects of mathematical logic and set theory have belonged to mathematics since the end of the 19th century. [52] [53] Before this period, sets were not considered to be mathematical objects, and logic, although used for mathematical proofs, belonged to philosophy and was not specifically studied by mathematicians. [54] Areas of mathematics used in the social sciences include probability/statistics and differential equations ( stochastic or deterministic). [ citation needed] These areas are used in fields such as sociology, [143] psychology, [144] economics, finance, and linguistics. [ citation needed] Supply and demand curves, like this one, are a staple of mathematical economics.Number theory is a branch of pure mathematics devoted primarily to the study of the integers and integer-valued functions. German mathematician Carl Friedrich Gauss said, "Mathematics is the queen of the sciences—and number theory is the queen of mathematics." a b Warner, Evan (2013). "Splash Talk: The Foundational Crisis of Mathematics" (PDF). Columbia University. pp.1–17. Archived (PDF) from the original on April 14, 2021 . Retrieved November 4, 2022. Numerical analysis, mainly devoted to the computation on computers of solutions of ordinary and partial differential equations that arise in many applications. Both meanings can be found in Plato, the narrower in Republic. 510c. "Plato, Republic, Book 6, section 510c". Archived from the original on February 24, 2021 . Retrieved June 19, 2019. {{ cite web}}: CS1 maint: bot: original URL status unknown ( link), but Plato did not use a math- word; Aristotle did, commenting on it. μαθηματική. Liddell, Henry George; Scott, Robert; A Greek–English Lexicon at the Perseus Project. OED Online. Mathematics.