The Essence of Mathematics Through Elementary Problems (Record no. 38938)
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| 000 -LEADER | |
|---|---|
| fixed length control field | 04743nam a2200373 i 4500 |
| 001 - CONTROL NUMBER | |
| control field | OTLid0000726 |
| 003 - CONTROL NUMBER IDENTIFIER | |
| control field | MnU |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20241120064019.0 |
| 006 - FIXED-LENGTH DATA ELEMENTS--ADDITIONAL MATERIAL CHARACTERISTICS--GENERAL INFORMATION | |
| fixed length control field | m o d s |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION | |
| fixed length control field | cr |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 190622s2019 mnu o 0 0 eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9781783747016 |
| 040 ## - CATALOGING SOURCE | |
| Original cataloging agency | MnU |
| Language of cataloging | eng |
| Transcribing agency | MnU |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER | |
| Classification number | QA37.3 |
| 245 04 - TITLE STATEMENT | |
| Title | The Essence of Mathematics Through Elementary Problems |
| Statement of responsibility, etc | Alexandre Borovik |
| 264 #2 - | |
| -- | Minneapolis, MN |
| -- | Open Textbook Library |
| 264 #1 - | |
| -- | [Place of publication not identified] |
| -- | Open Book Publishers |
| -- | [2019] |
| 264 #4 - | |
| -- | ©2019. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | 1 online resource |
| 336 ## - | |
| -- | text |
| -- | txt |
| -- | rdacontent |
| 337 ## - | |
| -- | computer |
| -- | c |
| -- | rdamedia |
| 338 ## - | |
| -- | online resource |
| -- | cr |
| -- | rdacarrier |
| 490 0# - SERIES STATEMENT | |
| Series statement | Open textbook library. |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | I. Mental Skills -- 1.1 Mental arithmetic and algebra -- 1.2 Direct and inverse procedures -- 1.3 Structural arithmetic -- 1.4 Pythagoras' Theorem -- 1.5 Visualisation -- 1.6 Trigonometry and radians -- 1.7 Regular polygons and regular polyhedra -- 1.8 Chapter 1: Comments and solutions -- II. Arithmetic -- 2.1 Place value and decimals: basic structure -- 2.2 Order and factors -- 2.3 Standard written algorithms -- 2.4 Divisibility tests -- 2.5 Sequences -- 2.6 Commutative, associative and distributive laws -- 2.7 Infinite decimal expansions -- 2.8 The binary numeral system -- 2.9 The Prime Number Theorem -- 2.10 Chapter 2: Comments and solutions -- III. Word Problems -- 3.1 Twenty problems which embody "3 - 1 = 2" -- 3.2 Some classical examples -- 3.3 Speed and acceleration -- 3.4 Hidden connections -- 3.5 Chapter 3: Comments and solutions -- IV. Algebra -- 4.1 Simultaneous linear equations and symmetry -- 4.2 Inequalities and modulus -- 4.3 Factors, roots, polynomials and surds -- 4.4 Complex numbers -- 4.5 Cubic equations -- 4.6 An extra -- 4.7 Chapter 4: Comments and solutions -- V. Geometry -- 5.1 Comparing geometry and arithmetic -- 5.2 Euclidean geometry: a brief summary -- 5.3 Areas, lengths and angles -- 5.4 Regular and semi-regular tilings in the plane -- 5.5 Ruler and compasses constructions for regular polygons -- 5.6 Regular and semi-regular polyhedra -- 5.7 The Sine Rule and the Cosine Rule -- 5.8 Circular arcs and circular sectors -- 5.9 Convexity -- 5.10 Pythagoras' Theorem in three dimensions -- 5.11 Loci and coonic sections -- 5.12 Cubes in higher dimensions -- 5.13 Chapter 5: Comments and solutions -- VI. Infinity: recursions, induction, infinite descent -- 6.1 Proof by mathematical induction I -- 6.2 'Mathematical induction' and 'scientific induction' -- 6.3 Proof by mathematical induction II -- 6.4 Infinite geometric series -- 6.5 Some classical inequalities -- 6.6 The harmonic series -- 6.7 Induction in geometry, combinatorics and number theory -- 6.8 Two problems -- 6.9 Infinite descent -- 6.10 Chapter 6: Comments and solutions |
| 520 0# - SUMMARY, ETC. | |
| Summary, etc | It is increasingly clear that the shapes of reality – whether of the natural world, or of the built environment – are in some profound sense mathematical. Therefore it would benefit students and educated adults to understand what makes mathematics itself ‘tick’, and to appreciate why its shapes, patterns and formulae provide us with precisely the language we need to make sense of the world around us. The second part of this challenge may require some specialist experience, but the authors of this book concentrate on the first part, and explore the extent to which elementary mathematics allows us all to understand something of the nature of mathematics from the inside. The Essence of Mathematics consists of a sequence of 270 problems – with commentary and full solutions. The reader is assumed to have a reasonable grasp of school mathematics. More importantly, s/he should want to understand something of mathematics beyond the classroom, and be willing to engage with (and to reflect upon) challenging problems that highlight the essence of the discipline. The book consists of six chapters of increasing sophistication (Mental Skills; Arithmetic; Word Problems; Algebra; Geometry; Infinity), with interleaved commentary. The content will appeal to students considering further study of mathematics at university, teachers of mathematics at age 14-18, and anyone who wants to see what this kind of elementary content has to tell us about how mathematics really works. |
| 542 1# - | |
| -- | Attribution |
| 546 ## - LANGUAGE NOTE | |
| Language note | In English. |
| 588 0# - | |
| -- | Description based on print resource |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Mathematics |
| Form subdivision | Textbooks |
| 700 1# - ADDED ENTRY--PERSONAL NAME | |
| Personal name | Borovik, Alexandre |
| Relator term | author |
| 700 1# - ADDED ENTRY--PERSONAL NAME | |
| Personal name | Gardiner, Tony |
| Relator term | author |
| 710 2# - ADDED ENTRY--CORPORATE NAME | |
| Corporate name or jurisdiction name as entry element | Open Textbook Library |
| Relator term | distributor |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | <a href="https://open.umn.edu/opentextbooks/textbooks/726">https://open.umn.edu/opentextbooks/textbooks/726</a> |
| Public note | Access online version |
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