標(biāo)題: Titlebook: Elements of Mathematics; A Problem-Centered A Gabor Toth Textbook 2021 The Editor(s) (if applicable) and The Author(s), under exclusive lic [打印本頁(yè)] 作者: Suture 時(shí)間: 2025-3-21 17:47
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書目名稱Elements of Mathematics讀者反饋
書目名稱Elements of Mathematics讀者反饋學(xué)科排名
作者: 背帶 時(shí)間: 2025-3-21 22:17 作者: 壕溝 時(shí)間: 2025-3-22 01:29
Rational and Real Exponentiation,s due to Besicovitch, the Young inequality, some sharp estimates on the .-series, equiconvergence through the Cauchy condensation test, power sums, and the lesser known method of (arithmetic) means. A short section on logarithms along with a few contest level problems is followed by a final section 作者: 敵意 時(shí)間: 2025-3-22 04:37
Real Analytic Plane Geometry, existence and properties of the circular arc length are shown using purely metric tools, and paving the way to trigonometry (Chapter .). This also gives a precise answer to the question: “What is .?” Once again, this relies on the Least Upper Bound Property of the real number system, the main commo作者: 補(bǔ)充 時(shí)間: 2025-3-22 12:36 作者: Senescent 時(shí)間: 2025-3-22 13:36
Rational and Algebraic Expressions and Functions,contest problems involving these means, we chose a representative sample to demonstrate the principal methods. The lesser known permutation (arrangement) inequality is also introduced here pointing out that it implies all the other classical inequalities such as the AM–GM, Cauchy–Schwarz (Sections .作者: Senescent 時(shí)間: 2025-3-22 19:51 作者: Cosmopolitan 時(shí)間: 2025-3-22 21:39
Eugenia Larjow,Christian Reuschenbachorresponding Bernoulli inequality. This opens the first opportunity to present a whole cadre of contest problems some of which are on Olympiad level. Working with the Dedekind model of the real number system is cumbersome, and not well suited to do analysis, however. We therefore build another model作者: MAIM 時(shí)間: 2025-3-23 04:06 作者: interference 時(shí)間: 2025-3-23 07:19
Laura Maa?,Xiange Zhang,Julian Gansen existence and properties of the circular arc length are shown using purely metric tools, and paving the way to trigonometry (Chapter .). This also gives a precise answer to the question: “What is .?” Once again, this relies on the Least Upper Bound Property of the real number system, the main commo作者: 迎合 時(shí)間: 2025-3-23 10:48
https://doi.org/10.1007/978-3-540-29465-8als (leading to a very simple but non-standard derivation of the quadratic formula), the Viète relations, and the Newton–Girard formulas for power sums. Among the many applications of the Viète relations, we give an arithmetic proof of the allegedly most challenging problem ever posted on the Intern作者: Arthropathy 時(shí)間: 2025-3-23 13:53 作者: Conducive 時(shí)間: 2025-3-23 20:42
Limits of Real Functions,eloped advanced differential calculus) mainly because the derivative as a limit is an indispensable tool for later developments. For future purposes, we also give quick proofs of the Extreme Values Theorem, the Intermediate Value Theorem, and the Fermat Principle.作者: 彈藥 時(shí)間: 2025-3-24 01:28
Trigonometry,e, circumcircle, and Heron’s formula (with an extremal property through the AM-GM inequality). One of the highlights of this chapter is Newton’s lesser known elementary approach (using means) to derive the power series of the sine and cosine functions well before the advent of the Taylor series.作者: CRATE 時(shí)間: 2025-3-24 03:45 作者: 的事物 時(shí)間: 2025-3-24 08:23
0172-6056 examples and problems inspired by mathematical contests.Ill.This 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 pa作者: liposuction 時(shí)間: 2025-3-24 11:13 作者: delusion 時(shí)間: 2025-3-24 15:33
Conics,thod of extracting square roots. Finally, we use symmetry properties of hyperbolas to present a geometric proof of the famous 1988 International Mathematical Olympiad problem discussed in Chapter . (Example .).作者: conformity 時(shí)間: 2025-3-24 19:01 作者: 羊齒 時(shí)間: 2025-3-25 01:38
Management im vernetzten Unternehmene, circumcircle, and Heron’s formula (with an extremal property through the AM-GM inequality). One of the highlights of this chapter is Newton’s lesser known elementary approach (using means) to derive the power series of the sine and cosine functions well before the advent of the Taylor series.作者: 殺死 時(shí)間: 2025-3-25 05:17 作者: surrogate 時(shí)間: 2025-3-25 08:27
Polynomial Functions,his chapter we return to algebra and study the roots of polynomials, once again with full details of the cubic case. We finish this chapter by the somewhat more advanced topic of multivariate factoring.作者: Thymus 時(shí)間: 2025-3-25 15:41 作者: endocardium 時(shí)間: 2025-3-25 18:48 作者: Ebct207 時(shí)間: 2025-3-25 22:36 作者: 少量 時(shí)間: 2025-3-26 00:53 作者: BOOST 時(shí)間: 2025-3-26 07:16
https://doi.org/10.1007/978-3-642-34795-5 are introduced using Peano’s system of axioms. Inherent in the last Peano axiom is his Principle of Induction, one of the fundamental postulates of arithmetic on natural numbers. Among the myriad of applications of this principle, we discuss here the Division Algorithm for Integers along with the g作者: 暴行 時(shí)間: 2025-3-26 11:54
Eugenia Larjow,Christian Reuschenbachleads naturally to Dedekind’s original proof of irrationality of the square root of a non-square natural number. As an immediate byproduct, this implies that the Least Upper Bound Property fails. Another advantage of this proof is that it leads directly to the concept of Dedekind cuts, and thereby t作者: 狼群 時(shí)間: 2025-3-26 16:41 作者: 很像弓] 時(shí)間: 2025-3-26 20:51
Informationsmanagement und Controlling, (arithmetic and analytic) properties of these functional limits can be derived by establishing their link with sequential limits. In our largely classical approach, continuity and differentiability of real functions are also introduced and treated here as special limits (stopping short of fully dev作者: ascetic 時(shí)間: 2025-3-26 23:40
Laura Maa?,Xiange Zhang,Julian Gansens path; and, in making use of the real number system already in place, we develop real analytic plane geometry using Birkhoff’s axioms of metric geometry. One of the main purposes of this chapter is to explain what is classically known as the Cantor–Dedekind Axiom: The real number system is order-is作者: 是突襲 時(shí)間: 2025-3-27 03:13
https://doi.org/10.1007/978-3-540-29465-8It is presented here with full arithmetic and historical details, with many identities, and along with its principal, mostly combinatorial, applications including Bernoulli’s derangements. The Division Algorithm for Integers discussed in Section . leads directly to its polynomial analogue, the Divis作者: Figate 時(shí)間: 2025-3-27 09:05
Management im Orientierungsdilemmas and monotonicity) for graphs of polynomial functions using synthetic division applied to difference quotients. We treat the difference quotient of a polynomial as a rational function with a removable singularity at the point where the quotient is taken. Removing the singularity then takes us direc作者: 作繭自縛 時(shí)間: 2025-3-27 13:02 作者: Counteract 時(shí)間: 2025-3-27 14:15 作者: hieroglyphic 時(shí)間: 2025-3-27 21:30 作者: Rheumatologist 時(shí)間: 2025-3-28 01:12 作者: 兇兆 時(shí)間: 2025-3-28 03:07
978-3-030-75053-4The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl作者: 畏縮 時(shí)間: 2025-3-28 10:00
Elements of Mathematics978-3-030-75051-0Series ISSN 0172-6056 Series E-ISSN 2197-5604 作者: BADGE 時(shí)間: 2025-3-28 11:42
https://doi.org/10.1007/978-3-030-75051-0Axiomatic mathematics before calculus; Axiomatic precalculus; Rigorous precalculus textbook; Mathematic作者: Liberate 時(shí)間: 2025-3-28 16:05 作者: paroxysm 時(shí)間: 2025-3-28 19:18
Preliminaries: Sets, Relations, Maps,In this chapter we give an account on the foundations of mathematics: na?ve and axiomatic set theory. We introduce here several concepts that will play principal roles later: The Least Upper Bound Property for ordered sets, relations, maps, infinite sequences, the principle of inclusion-exclusion, cardinality, and classes vs. sets.作者: 粘 時(shí)間: 2025-3-29 00:31
https://doi.org/10.1007/978-3-642-34795-5 are introduced using Peano’s system of axioms. Inherent in the last Peano axiom is his Principle of Induction, one of the fundamental postulates of arithmetic on natural numbers. Among the myriad of applications of this principle, we discuss here the Division Algorithm for Integers along with the greatest common divisor and prime factorization.作者: enmesh 時(shí)間: 2025-3-29 06:52 作者: Alpha-Cells 時(shí)間: 2025-3-29 09:06 作者: 生銹 時(shí)間: 2025-3-29 12:03
Real Numbers,leads naturally to Dedekind’s original proof of irrationality of the square root of a non-square natural number. As an immediate byproduct, this implies that the Least Upper Bound Property fails. Another advantage of this proof is that it leads directly to the concept of Dedekind cuts, and thereby t作者: FAST 時(shí)間: 2025-3-29 18:48
Rational and Real Exponentiation, arithmetic properties of the limit inferior and limit superior and (thereby) the limit. The Fibonacci sequence, the geometric and .-series, and some of their contest level offsprings serve here as illustrations. The core material of this chapter proves the existence of roots of (positive) real numb作者: HAWK 時(shí)間: 2025-3-29 22:33 作者: 服從 時(shí)間: 2025-3-30 00:12
Real Analytic Plane Geometry,s path; and, in making use of the real number system already in place, we develop real analytic plane geometry using Birkhoff’s axioms of metric geometry. One of the main purposes of this chapter is to explain what is classically known as the Cantor–Dedekind Axiom: The real number system is order-is作者: Erythropoietin 時(shí)間: 2025-3-30 05:10
Polynomial Expressions,It is presented here with full arithmetic and historical details, with many identities, and along with its principal, mostly combinatorial, applications including Bernoulli’s derangements. The Division Algorithm for Integers discussed in Section . leads directly to its polynomial analogue, the Divis作者: Accede 時(shí)間: 2025-3-30 09:21
Polynomial Functions,s and monotonicity) for graphs of polynomial functions using synthetic division applied to difference quotients. We treat the difference quotient of a polynomial as a rational function with a removable singularity at the point where the quotient is taken. Removing the singularity then takes us direc作者: CURL 時(shí)間: 2025-3-30 13:00
Conics,rties of them with applications and full historical details. We show how parabolas can be used to give a geometric interpretation of the Babylonian method of extracting square roots. Finally, we use symmetry properties of hyperbolas to present a geometric proof of the famous 1988 International Mathe作者: MURKY 時(shí)間: 2025-3-30 17:44 作者: 連詞 時(shí)間: 2025-3-30 23:22 作者: 擴(kuò)音器 時(shí)間: 2025-3-31 01:33
