001439920 000__ 04274cam\a2200565\i\4500
001439920 001__ 1439920
001439920 003__ OCoLC
001439920 005__ 20230309004530.0
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001439920 019__ $$a1269201794$$a1273001315
001439920 020__ $$a9783030750510$$q(electronic bk.)
001439920 020__ $$a3030750515$$q(electronic bk.)
001439920 020__ $$z9783030750503
001439920 020__ $$z3030750507
001439920 0247_ $$a10.1007/978-3-030-75051-0$$2doi
001439920 035__ $$aSP(OCoLC)1269094774
001439920 040__ $$aYDX$$beng$$erda$$epn$$cYDX$$dGW5XE$$dEBLCP$$dOCLCO$$dOCLCF$$dN$T$$dOCLCQ$$dCOM$$dOCLCO$$dSFB$$dOCLCQ
001439920 049__ $$aISEA
001439920 050_4 $$aQA39.3$$b.T68 2021
001439920 08204 $$a510$$223
001439920 1001_ $$aTóth, Gábor,$$cPh. D.,$$eauthor.
001439920 24510 $$aElements of mathematics :$$ba problem-centered approach to history and foundations /$$cGabor Toth.
001439920 264_1 $$aCham :$$bSpringer,$$c[2021]
001439920 264_4 $$c©2021
001439920 300__ $$a1 online resource :$$billustrations (some color)
001439920 336__ $$atext$$btxt$$2rdacontent
001439920 337__ $$acomputer$$bc$$2rdamedia
001439920 338__ $$aonline resource$$bcr$$2rdacarrier
001439920 4901_ $$aUndergraduate texts in mathematics. Readings in mathematics
001439920 504__ $$aIncludes bibliographical references and index.
001439920 5050_ $$a0. Preliminaries: Sets, Relations, Maps -- 1. Natural, Integral and Rational Numbers -- 2. Real Numbers -- 3. Rational and Real Exponentiation -- 4. Limits of Real Functions -- 5. Real Analytic Plane Geometry -- 6. Polynomial Expressions -- 7. Polynomial Functions -- 8. Conics -- 9. Rational and Algebraic Expressions and Functions -- 10. Exponential and Logarithmic Functions -- 11. Trigonometry -- Further Reading -- Index.
001439920 506__ $$aAccess limited to authorized users.
001439920 520__ $$aThis textbook offers a rigorous presentation of mathematics before the advent of calculus. Fundamental concepts in algebra, geometry, and number theory are developed from the foundations of set theory along an elementary, inquiry-driven path. Thought-provoking examples and challenging problems inspired by mathematical contests motivate the theory, while frequent historical asides reveal the story of how the ideas were originally developed. Beginning with a thorough treatment of the natural numbers via Peano's axioms, the opening chapters focus on establishing the natural, integral, rational, and real number systems. Plane geometry is introduced via Birkhoff's axioms of metric geometry, and chapters on polynomials traverse arithmetical operations, roots, and factoring multivariate expressions. An elementary classification of conics is given, followed by an in-depth study of rational expressions. Exponential, logarithmic, and trigonometric functions complete the picture, driven by inequalities that compare them with polynomial and rational functions. Axioms and limits underpin the treatment throughout, offering not only powerful tools, but insights into non-trivial connections between topics. Elements of Mathematics is ideal for students seeking a deep and engaging mathematical challenge based on elementary tools. Whether enhancing the early undergraduate curriculum for high achievers, or constructing a reflective senior capstone, instructors will find ample material for enquiring mathematics majors. No formal prerequisites are assumed beyond high school algebra, making the book ideal for mathematics circles and competition preparation. Readers who are more advanced in their mathematical studies will appreciate the interleaving of ideas and illuminating historical details.
001439920 588__ $$aOnline resource; title from PDF title page (SpringerLink, viewed October 5, 2021).
001439920 650_0 $$aMathematics.
001439920 650_0 $$aMathematics$$xHistory.
001439920 650_6 $$aMathématiques.
001439920 650_6 $$aMathématiques$$xHistoire.
001439920 655_7 $$aHistory.$$2fast$$0(OCoLC)fst01411628
001439920 655_0 $$aElectronic books.
001439920 77608 $$iPrint version:$$z3030750507$$z9783030750503$$w(OCoLC)1245656403
001439920 830_0 $$aUndergraduate texts in mathematics.$$pReadings in mathematics.
001439920 852__ $$bebk
001439920 85640 $$3Springer Nature$$uhttps://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-3-030-75051-0$$zOnline Access$$91397441.1
001439920 909CO $$ooai:library.usi.edu:1439920$$pGLOBAL_SET
001439920 980__ $$aBIB
001439920 980__ $$aEBOOK
001439920 982__ $$aEbook
001439920 983__ $$aOnline
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