國立高雄大學圖資館 |

語系: 繁體中文

說明(常見問題)

圖資館首頁

登入

回首頁

切換: 標籤 | MARC模式 | ISBD

Elements of mathematicsa problem-cen...

SpringerLink (Online service)

Elements of mathematicsa problem-centered approach to history and foundations /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Elements of mathematicsby Gabor Toth.
其他題名:	a problem-centered approach to history and foundations /
作者:	Toth, Gabor.
出版者:	Cham :Springer International Publishing :2021.
面頁冊數:	xv, 527 p. :ill. (some col.), digital ;24 cm.
Contained By:	Springer Nature eBook
標題:	Mathematics.
電子資源:	https://doi.org/10.1007/978-3-030-75051-0
ISBN:	9783030750510$q(electronic bk.)

Elements of mathematicsa problem-centered approach to history and foundations /
Toth, Gabor.

Elements of mathematicsa problem-centered approach to history and foundations /[electronic resource] :by Gabor Toth. - Cham :Springer International Publishing :2021. - xv, 527 p. :ill. (some col.), digital ;24 cm. - Undergraduate texts in mathematics. Readings in mathematics. - Undergraduate texts in mathematics.Readings in mathematics..

0. 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.

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 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.

ISBN: 9783030750510$q(electronic bk.)

Standard No.: 10.1007/978-3-030-75051-0doiSubjects--Topical Terms:

184409
Mathematics.

LC Class. No.: QA39.3 / .T68 2021

Dewey Class. No.: 510

Elements of mathematicsa problem-centered approach to history and foundations /
LDR:03317nmm a2200337 a 4500 001 609633
003 DE-He213
005 20210923112221.0
006 m d
007 cr nn 008maaau
008 220222s2021 sz s 0 eng d
020 $a 9783030750510$q(electronic bk.)
020 $a 9783030750503$q(paper)
024 7 $a 10.1007/978-3-030-75051-0 $2 doi
035 $a 978-3-030-75051-0
040 $a GP $c GP
041 0 $a eng
050 4 $a QA39.3 $b .T68 2021
072 7 $a PBKB $2 bicssc
072 7 $a MAT034000 $2 bisacsh
072 7 $a PBKB $2 thema
082 0 4 $a 510 $2 23
090 $a QA39.3 $b .T717 2021
100 1 $a Toth, Gabor. $3 469462
245 1 0 $a Elements of mathematics $h [electronic resource] : $b a problem-centered approach to history and foundations / $c by Gabor Toth.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2021.
300 $a xv, 527 p. : $b ill. (some col.), digital ; $c 24 cm.
490 1 $a Undergraduate texts in mathematics. Readings in mathematics
505 0 $a 0. 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.
520 $a 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 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.
650 0 $a Mathematics. $3 184409
650 0 $a Mathematics $x History. $3 189740
650 1 4 $a Real Functions. $3 273779
650 2 4 $a Number Theory. $3 274059
650 2 4 $a Field Theory and Polynomials. $3 274058
650 2 4 $a Geometry. $3 183883
650 2 4 $a History of Mathematical Sciences. $3 511733
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer Nature eBook
830 0 $a Undergraduate texts in mathematics. $p Readings in mathematics. $3 907324
856 4 0 $u https://doi.org/10.1007/978-3-030-75051-0
950 $a Mathematics and Statistics (SpringerNature-11649)