Atnaujinkite slapukų nuostatas

El. knyga: Introduction to Experimental Mathematics

3.00/5 (2 ratings by Goodreads)
(University of Copenhagen), (University of Copenhagen)
Kitos knygos pagal šią temą:
Introduction to Experimental MathematicsDidesnis paveikslėlis
Kitos knygos pagal šią temą:

DRM apribojimai

  • Kopijuoti:

    neleidžiama

  • Spausdinti:

    neleidžiama

  • El. knygos naudojimas:

    Skaitmeninių teisių valdymas (DRM)
    Leidykla pateikė šią knygą šifruota forma, o tai reiškia, kad norint ją atrakinti ir perskaityti reikia įdiegti nemokamą programinę įrangą. Norint skaityti šią el. knygą, turite susikurti Adobe ID . Daugiau informacijos  čia. El. knygą galima atsisiųsti į 6 įrenginius (vienas vartotojas su tuo pačiu Adobe ID).

    Reikalinga programinė įranga
    Norint skaityti šią el. knygą mobiliajame įrenginyje (telefone ar planšetiniame kompiuteryje), turite įdiegti šią nemokamą programėlę: PocketBook Reader (iOS / Android)

    Norint skaityti šią el. knygą asmeniniame arba „Mac“ kompiuteryje, Jums reikalinga  Adobe Digital Editions “ (tai nemokama programa, specialiai sukurta el. knygoms. Tai nėra tas pats, kas „Adobe Reader“, kurią tikriausiai jau turite savo kompiuteryje.)

    Negalite skaityti šios el. knygos naudodami „Amazon Kindle“.

A recent surge in computer-based experimental approaches to pure mathematics is revolutionizing the way research mathematicians work. As the first of its kind, this textbook provides students with an introduction to the ends and means of experimental mathematics using the popular computer algebra system Maple.

Mathematics is not, and never will be, an empirical science, but mathematicians are finding that the use of computers and specialized software allows the generation of mathematical insight in the form of conjectures and examples, which pave the way for theorems and their proofs. In this way, the experimental approach to pure mathematics is revolutionizing the way research mathematicians work. As the first of its kind, this book provides material for a one-semester course in experimental mathematics that will give students the tools and training needed to systematically investigate and develop mathematical theory using computer programs written in Maple. Accessible to readers without prior programming experience, and using examples of concrete mathematical problems to illustrate a wide range of techniques, the book gives a thorough introduction to the field of experimental mathematics, which will prepare students for the challenge posed by open mathematical problems.

Recenzijos

'I'd like to applaud the authors for their interesting, innovative, well-structured book that is sure to serve as a standard for some time against which other future books of a similar kind will be measured against.' Michael de Villiers, The Mathematical Gazette

Daugiau informacijos

This text introduces students to an experimental approach to mathematics, using Maple to systematically investigate and develop mathematical theory.
Preface ix
About This Book ix
For the Student x
For the Teacher x
About Maple xi
The Contents of This Book xii
Exercises and Projects xiv
Acknowledgements xv
1 Experimental Method
1(18)
1.1 Experimenting with Mathematics
1(4)
1.2 Basic Methodology
5(2)
1.3 From Hypothesis to Proof
7(1)
1.4 Keeping Experiments Honest
8(1)
1.5 Dangers
9(4)
1.6 Case Studies
13(4)
1.7 Exercises
17(1)
1.8 Notes and Further Reading
18(1)
2 Basic Programming in Maple
19(32)
2.1 Statements, Execution and Groups
19(1)
2.2 Variables, Functions and Expressions
20(2)
2.3 Sets, Lists, Sequences, Matrices and Strings
22(2)
2.4 Control Structures
24(4)
2.5 Procedures
28(8)
2.6 Pseudocode and Stepwise Refinement
36(4)
2.7 Errors
40(2)
2.8 Automated Testing of Hypotheses
42(3)
2.9 Exercises
45(4)
2.10 Notes and Further Reading
49(2)
3 Iteration and Recursion
51(42)
3.1 Iteration versus Recursion
51(4)
3.2 Iteration
55(10)
3.3 Recursion
65(8)
3.4 Knowing When to Stop
73(15)
3.5 Exercises
88(4)
3.6 Notes and Further Reading
92(1)
4 Visualization
93(39)
4.1 Plotting Data
93(19)
4.2 Fitting
112(11)
4.3 Probability Distributions
123(1)
4.4 Exercises
124(7)
4.5 Notes and Further Reading
131(1)
5 Symbolic Inversion
132(70)
5.1 Overview
132(22)
5.2 Recognizing Integer Sequences
154(11)
5.3 Recognizing Floating-point Numbers
165(11)
5.4 The Mathematics of Inversion
176(6)
5.5 Case Studies
182(9)
5.6 Exercises
191(9)
5.7 Notes and Further Reading
200(2)
6 Pseudorandomness
202(31)
6.1 Why Use Randomness?
202(1)
6.2 True Randomness vs. Pseudorandomness
203(1)
6.3 Pseudorandom Number Generators
204(5)
6.4 Pseudorandomness in Maple
209(5)
6.5 Using Pseudorandomness in Experiments
214(9)
6.6 Randomness in Algorithms
223(4)
6.7 Exercises
227(4)
6.8 Notes and Further Reading
231(2)
7 Time, Memory and Precision
233(31)
7.1 Order of Consumption
233(7)
7.2 Balancing Time and Memory
240(2)
7.3 Maple-specific Efficiency Tips
242(4)
7.4 Floating-point Precision
246(11)
7.5 Exercises
257(6)
7.6 Notes and Further Reading
263(1)
8 Applications of Linear Algebra and Graph Theory
264(27)
8.1 Graphs
264(6)
8.2 Linear Algebra
270(4)
8.3 Generalizations and Variations of Graphs
274(3)
8.4 Generic Linear Algebra in Maple
277(3)
8.5 Isomorphism and Equivalence
280(4)
8.6 Exercises
284(4)
8.7 Notes and Further Reading
288(3)
Illustration notes 291(2)
References 293(6)
Index 299
Sųren Eilers is a professor of mathematics at the University of Copenhagen who heads the VILLUM Foundation Network for Experimental Mathematics in Number Theory, Operator Algebras, and Topology. He has received numerous teaching prizes as well as an outreach prize for developing the mathematics of LEGO, and is an expert of the classification of C*-algebras. Rune Johansen was the first postdoc in experimental mathematics in Denmark, specializing in symbolic dynamics.
Daugiau apie elektronines knygas Daugiau apie elektronines knygas
Pastovi nuoroda: https://www.kriso.lt/db/97811081320776e.html
Raktažodžiai: