WULOLIFE
Subtitle of Wu Jun's General Mathematics Lectures: It turns out that mathematics can be used in this way Author: Wu Jun
Subtitle of Wu Jun's General Mathematics Lectures: It turns out that mathematics can be used in this way Author: Wu Jun
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Description
Introduction · · · · · ·
How can you spot a Ponzi scheme and manage your finances and investments? How can you make the best choice when applying for a home loan? How can you increase the chances of your resume passing the initial screening? How can you plan your company's development curve? More importantly, how can you improve your level of cognition? How can you change your way of thinking?
If you are also concerned about these issues and hope to use mathematical thinking to better improve yourself and understand the world, I hope you will read this book.
This is a general mathematics handout for everyone. The book connects the entire mathematics system through key knowledge points to help you gradually build your own mathematical knowledge structure. The history of mathematics development throughout the book is actually the history of human cognition development. You can use it to gradually train your cognition: from intuitive to abstract, from static to dynamic, from macro to micro, from random to certain and then to random.
For readers majoring in science and engineering, this book can help you better sort out your previous mathematical knowledge and look at mathematics and the human knowledge system more comprehensively from a higher perspective; for readers who are not majoring in science and engineering, this book can help you better train your mathematical thinking, allowing you to get to the essence, simplify things, and make correct decisions.
About the Author · · · · · ·
Wu Jun
PhD, well-known natural language processing and search expert, Silicon Valley venture capitalist. His book The Beauty of Mathematics won the 8th Wenjin Book Award of the National Library and the 5th China Excellent Publications Award, The Light of Civilization was named a 2014 "China Good Book", and The Top of the Wave won the "Blue Lion 2011 Top Ten Excellent Business Books" Award.
Dr. Wu Jun was a researcher at Google and designed Google's Chinese, Japanese and Korean search algorithms as well as Google's natural language analyzer. From 2010 to 2012, he served as Tencent's vice president in charge of search and search advertising, and later returned to Google to lead the computer automatic question answering project.
Dr. Wu Jun has been engaged in venture capital since 2008 and founded Silicon Valley Fengyuan Capital Venture Capital Fund as a founding partner in 2014. He is also a visiting researcher at Shanghai Jiao Tong University and a director of the Johns Hopkins University School of Engineering.
Table of contents · · · · · ·
Preface 009
Basics Chapter 1 Clues to Understanding Mathematics: Starting with Pythagoras
1.1 Pythagorean Theorem: Why is it called the Pythagorean Theorem in the West?
1.2 Mathematical Predictability: Irrational Numbers are a Corollary of the Pythagorean Theorem
1.3 Mathematical thinking: How to think logically 036
1.4 Golden Section: The Bridge between Mathematics and Aesthetics045
1.5 Optimization method: Hua Luogeng's masterstroke of simplifying complexity058
Chapter 2 Sequences and Series: Key Contents that Connect the Previous and Next
2.1 Mathematical Relevance: Fibonacci Sequence and Golden Ratio
2.2 Changes in the number series: Trends are more important than the present
2.3 Series: Mathematical Principles in MLM Scams079
2.4 Geometric progression: pay half the interest and get twice the return
Chapter 3 The Boundaries of Mathematics: Is Mathematics Universal?
3.1 The Limits of Mathematics: From Goetheorem to Fermat's Last Theorem 104
3.2 Exploring the boundaries of mathematics: starting from Hilbert’s tenth problem108
Digital Chapter 4 Equations: New Methods and New Thinking
4.1 Chicken and rabbit in the same cage problem: What is the use of equations?
4.2 The solution of a cubic equation: a famous dispute over invention rights in the history of mathematics 126
4.3 Imaginary Numbers: What is the Use of Imaginary Tools? 135
Chapter 5 Infinitesimal and Infinitesimal: From Numbers to Trends
5.1 Infinity: Why is it so hard for us to understand an infinitely large world? 143
5.2 Infinitesimals: Zeno's paradox and its solution 149
5.3 The Second Mathematical Crisis: The Debate between Newton and Berkeley 156
5.4 Limits: Rethinking the World of the Infinitely Small 163
5.5 Dynamic Trend: Can Infinity and Infinitesimal Be Compared?
Geometry Chapter 6 Basic Geometry: The Establishment of Axiomatic System
6.1 The origins of geometry: why is geometry the oldest branch of mathematics?
6.2 Axiomatic System: Where Does the Systematic Theory of Geometry Come From? 194
Chapter 7 The Development of Geometry: A Pioneering Integration of Different Branches of Mathematics
7.1 Non-Euclidean Geometry: Will Geometry Collapse If We Change One Axiom?
7.2 Pi: The significance of a mathematical tool 214
7.3 Analytic Geometry: How to Solve Geometric Problems Using Algebraic Methods 221
7.4 The significance of the system: why geometry can provide a theoretical basis for law 232
Algebra Chapter 8 Functions: Important Mathematical Tools
8.1 Definition and Essence: From Static to Dynamic, From Quantity to Trend 244
8.2 Causation: the difference between determination and correlation 253
Chapter 9 Linear Algebra: A Tool More Useful Than You Think
9.1 Vectors: Direction of Quantity and Formation of Resultant Force 262
9.2 Law of Cosines: Text Classification and Resume Screening 278
9.3 Matrix: Application of Multidimensional Thinking 284
Calculus Chapter 10 Differentiation: How to understand the relationship between macro and micro
10.1 Derivatives: revealing new laws of change 300
10.2 Differentiation: A tool for describing the microscopic world 307
10.3 Singularity: Continuity and smoothness of change are the basis of stability 312
Chapter 11 Integration: Understanding Macro Trends from Micro Changes
11.1 Integration: The inverse of differentiation 323
11.2 The meaning of integration: understanding the whole from the details 327
11.3 Optimization Problems: Looking at Maximum and Minimum Values from a Changing Perspective 333
11.4 The dispute over the right of invention: the respective contributions of Newton and Leibniz 342
*11.5 Improvement of the system: the process of axiomatization of calculus 348
Probability and Mathematical Statistics Chapter 12 Randomness and Probability Theory: How to View Uncertainty
12.1 Probability Theory: A Gambler's Science 364
12.2 Classical Probability: Laplace's Systematic Theory of Probability 366
12.3 Bernoulli Experiment: What Does Randomness Really Mean? 371
12.4 Mean and Variance: The Gap between Ideal and Reality 378
Chapter 13 Small Probabilities and Large Probabilities: How to Share Resources and Eliminate Uncertainty
13.1. Poisson Distribution: Why Insurance Companies Must Have a Large Customer Base 386
13.2 Gaussian Distribution: What does a high probability event mean? 393
*13.3 Probability Axiomatization: The Unification of Theory and Reality 404
Chapter 14 Prerequisites: A New Way to Measure Randomness
14.1 Preconditions: The Effect of Conditions on Randomness 415
14.2 Differences: Probability, Joint Probability, and Conditional Probability 421
14.3 Relevance: Applications of Conditional Probability in Information Processing 430
14.4 Bayesian Theory: How Machine Translation Works 433
Chapter 15 Statistics and Data Methods: Prerequisites for Accurate Probability Estimates
15.1 Definition: What is Statistics? 442
15.2 Practice: How to do good statistics 446
15.3 Goode-Turing Discount Estimates: How to Prevent Black Swan Events 450
15.4 Look at the world from a different perspective: Probability is a worldview, statistics is a methodology 459
Chapter 16: The Place of Mathematics in the Human Knowledge System
16.1 Mathematics and philosophy: two disciplines at the same head and tail 468
16.2 Mathematics and Natural Science: How Mathematics Transforms Natural Science 474
16.3 Mathematics and Logic: Why Logic is the Foundation of Everything 480
16.4 Mathematics and other disciplines: Why mathematics is a more basic tool 486
16.5 Future Prospects: Hilbert's Lectures 493
Appendix Appendix 1 How much is the golden ratio?
Appendix 2 Why the ratio of two consecutive Fibonacci numbers converges to the golden ratio 498
Appendix 3 Geometric Series Sum Algorithm 500
Appendix 4 Solutions of the Nth-order Equation x N = 1 501
Appendix 5 Two other methods of calculating integrals 503
Appendix 6 The Law of Large Numbers 505
Appendix 7 English translation of Hilbert's retirement speech 507
Chapter 16: The Place of Mathematics in the Human Knowledge System
21.1 Mathematics and Philosophy/458
21.2 Mathematics and Natural Sciences/465
21.3 Mathematics and Logic / 469
21.4 Mathematics and other subjects/473
21.5 The famous mathematician Hilbert's speech before retirement / 478
