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Readable Introduction to Real Mathematics Softcover reprint of the original 1st ed. 2014 [Minkštas viršelis]

4.50/5 (6 ratings by Goodreads)
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  • Formatas: Paperback / softback, 161 pages, aukštis x plotis: 235x155 mm, weight: 2759 g, 50 Illustrations, black and white; XII, 161 p. 50 illus., 1 Paperback / softback
  • Serija: Undergraduate Texts in Mathematics
  • Išleidimo metai: 17-Sep-2016
  • Leidėjas: Springer International Publishing AG
  • ISBN-10: 331937950X
  • ISBN-13: 9783319379500
Kitos knygos pagal šią temą:
Readable Introduction to Real Mathematics Softcover reprint of the original 1st ed. 2014Didesnis paveikslėlis
  • Formatas: Paperback / softback, 161 pages, aukštis x plotis: 235x155 mm, weight: 2759 g, 50 Illustrations, black and white; XII, 161 p. 50 illus., 1 Paperback / softback
  • Serija: Undergraduate Texts in Mathematics
  • Išleidimo metai: 17-Sep-2016
  • Leidėjas: Springer International Publishing AG
  • ISBN-10: 331937950X
  • ISBN-13: 9783319379500
Kitos knygos pagal šią temą:
Pastovi nuoroda: https://www.kriso.lt/db/9783319379500.html
Raktažodžiai:

Designed for an undergraduate course or for independent study, this textbook presents sophisticated mathematical ideas in an elementary and friendly fashion. It features techniques to solve proofs as well as exercises of varying difficulty.



Designed for an undergraduate course or for independent study, this textbook presents sophisticated mathematical ideas in an elementary and friendly fashion. It features techniques to solve proofs as well as exercises of varying difficulty.



Designed for an undergraduate course or for independent study, this text presents sophisticated mathematical ideas in an elementary and friendly fashion. The fundamental purpose of this book is to engage the reader and to teach a real understanding of mathematical thinking while conveying the beauty and elegance of mathematics. The text focuses on teaching the understanding of mathematical proofs. The material covered has applications both to mathematics and to other subjects. The book contains a large number of exercises of varying difficulty, designed to help reinforce basic concepts and to motivate and challenge the reader. The sole prerequisite for understanding the text is basic high school algebra; some trigonometry is needed for Chapters 9 and 12. Topics covered include: mathematical induction - modular arithmetic - the fundamental theorem of arithmetic - Fermat's little theorem - RSA encryption - the Euclidean algorithm -rational and irrational numbers - complex numbers - cardinality - Euclidean plane geometry - constructability (including a proof that an angle of 60 degrees cannot be trisected with a straightedge and compass). This textbook is suitable for a wide variety of courses and for a broad range of students in the fields of education, liberal arts, physical sciences and mathematics. Students at the senior high school level who like mathematics will also be able to further their understanding of mathematical thinking by reading this book.

Recenzijos

It is carefully written in a precise but readable and engaging style and is tightly organised into eight short core chapters and four longer standalone extension chapters. I thoroughly enjoyed reading this recent addition to the Springer Undergraduate Texts in Mathematics series and commend this clear, well-organised, unfussy text to its target audiences. (Nick Lord, The Mathematical Gazette, Vol. 100 (547), 2016)

The book is an introduction to real mathematics and is very readable. The book is indeed a joy to read, and would be an excellent text for an appreciation of mathematics course, among other possibilities. (G. A. Heuer, Mathematical Reviews, February, 2015)

Daniel Rosenthal and Peter Rosenthal (both, Univ. of Toronto) and David Rosenthal (St. John's Univ.) present well-chosen, basic, conceptual mathematics, suitably accessible after a K-12 education, in a detailed, self-conscious way that emphasizes methodology alongside content and crucially leads to an ultimate clear payoff. Summing Up: Recommended. Lower-division undergraduates and two-year technical program students; general readers. (D. V. Feldman, Choice, Vol. 52 (6), February, 2015)

1 Introduction to the Natural Numbers
1(8)
1.1 Prime Numbers
2(3)
1.2 Unanswered Questions
5(1)
1.3 Problems
6(3)
2 Mathematical Induction
9(14)
2.1 The Principle of Mathematical Induction
9(7)
2.2 The Principle of Complete Mathematical Induction
16(5)
2.3 Problems
21(2)
3 Modular Arithmetic
23(8)
3.1 The Basics
23(2)
3.2 Some Applications
25(2)
3.3 Problems
27(4)
4 The Fundamental Theorem of Arithmetic
31(4)
4.1 Proof of the Fundamental Theorem of Arithmetic
31(2)
4.2 Problems
33(2)
5 Fermat's Theorem and Wilson's Theorem
35(6)
5.1 Fermat's Theorem
35(2)
5.2 Wilson's Theorem
37(2)
5.3 Problems
39(2)
6 Sending and Receiving Secret Messages
41(6)
6.1 The RSA Method
42(3)
6.2 Problems
45(2)
7 The Euclidean Algorithm and Applications
47(14)
7.1 The Euclidean Algorithm
48(1)
7.2 Applications
49(9)
7.3 Problems
58(3)
8 Rational Numbers and Irrational Numbers
61(10)
8.1 Rational Numbers
61(3)
8.2 Irrational Numbers
64(4)
8.3 Problems
68(3)
9 The Complex Numbers
71(14)
9.1 What is a Complex Number?
71(3)
9.2 The Complex Plane
74(5)
9.3 The Fundamental Theorem of Algebra
79(4)
9.4 Problems
83(2)
10 Sizes of Infinite Sets
85(24)
10.1 Cardinality
85(4)
10.2 Countable Sets and Uncountable Sets
89(4)
10.3 Comparing Cardinalities
93(13)
10.4 Problems
106(3)
11 Fundamentals of Euclidean Plane Geometry
109(18)
11.1 Triangles
109(5)
11.2 The Parallel Postulate
114(3)
11.3 Areas of Triangles
117(5)
11.4 Problems
122(5)
12 Constructability
127(32)
12.1 Constructions with Straightedge and Compass
128(3)
12.2 Constructible Numbers
131(6)
12.3 Surds
137(9)
12.4 Constructions of Geometric Figures
146(7)
12.5 Problems
153(6)
Index 159
Daniel Rosenthal is a mathematics student at the University of Toronto. David Rosenthal is Associate Professor of Mathematics at St. John's University in New York City. Peter Rosenthal is Professor Emeritus of Mathematics at the University of Toronto.