The Turing Advanced Mathematics book is divided into 8 categories of 19 independent books + three sets of books (this list will continue to add excellent books), most of which are crafted by world-class mathematical masters, they are classic, or popular, belong to the advanced mathematics reference books of the best works. For students, these books are prescribed by internationally renowned universities, with rich examples and covering multidisciplinary applications; For working people, these books are a great choice for self-study. They are easy to read and easy to understand.

Turing advanced Mathematics book List learning roadmap

Turing Advanced Mathematics Book List Learning Roadmap ** (text version) **

  • A. set of books

  • Princeton reader

  • Princeton Calculus Reader (revised Edition)

  • Princeton Reader on Probability Theory

  • Princeton Mathematical Analysis reader

  • Programmer math

  • Mathematics for Programmers (2nd edition)

  • Math for programmers 2: Probability statistics

  • Math for programmers 3: Linear Algebra

  • Turing Mathematical Classics

  • 01 Basic Topology (Revised)

  • 02 Pure Mathematics Course (9th edition)

  • 03 Inequalities (2nd edition)

  • 04 Matrix Calculation (4th edition)

  • Complex analysis: visualization method

  • B. calculus

  • Introduction to Calculus (revised Edition)

  • Simple Calculus: A super easy introductory technique not taught in school

  • C. probability theory

  • Introduction to Probability (2nd edition · Revised Edition)

  • Applying Stochastic Processes: An Introduction to Probabilistic Models (11th edition)

  • Probability Theory and Its Applications (Volume 1• 3rd Ed.)

  • [D]

  • This is how Linear Algebra should be learned (3rd edition)

  • Calculation of Matrices (In English • 4th edition)

  • Matrix Analysis (2nd Edition)

  • E. Mathematical analysis

  • Lectures 8 on Mathematical Analysis (Revised Edition)

  • Tao Zhexuan’s Real Analysis (3rd Edition)

  • F. Mathematical statistics

  • Sparse statistical learning and its application

  • Core methods of statistics and their applications

  • G. Computer mathematics

  • Concrete Mathematics: Fundamentals of Computer Science (2nd Ed.)

  • Mathematics in Vernacular machine learning

  • Mathematics of deep learning

  • Practical statistics for data scientists

  • The mathematics and physics of game development

  • H. other

  • Financial Time Series Analysis (3rd Edition)

  • Wavelet ten

A. set of books

1. The Princeton Three Musketeers

A math classic that is popular with math lovers

Princeton Calculus Reader

Author: Adrian banner | translator: Yang Shuang Zhao Xiaoting Gao Pu

Princeton Reader on Probability Theory

Author: Steven j. miller | translator: Li Xin

Princeton Mathematical Analysis Reader

Author: lafite Glenn berg | translator: Li Xin

The Princeton calculus on expounds the techniques for solving differential and integral calculus, detailed explained the foundation of calculus, limits and continuity, differential, the application of derivative, integral, infinite series, Taylor series and power series, etc, is designed to teach readers how to ponder over a problem to find the problem solving the required knowledge, focus on training people’s ability to solve problems.

The Princeton probability theory on book explain the basics of probability theory including portfolio analysis, probability, conditional probability, discrete random variable, continuous random variables, the nature of the joint distribution of random variables, expectations, limit theorem and simulation, etc., rich in content and easy to understand, with abundant examples and exercises in great quantities, Involving physics, biology, chemistry, genetics, game theory, economics and many other applications, very inspiring.

The Princeton Mathematical Analysis Reader covers the basics of learning real analysis, including basic mathematics and logic, real numbers, sets, topology, sequences, and more. In an easy and humorous way, the author describes the two-step method: first showing how to go back to the key to solving the problem, and then showing how to write down the process in a rigorous way. The book also gives rich examples to help students consolidate what they have learned.

2. The Programmer’s Math trilogy

Super popular Japanese programmer math series

Author: “city hao | translator: GuanJie, Lu Xiaona

Author: flat and luckily, Mr Xuan | translator: Chen Xiaoyan

Author: flat and luckily, Mr Xuan | translator: Lu Xiaona

The first edition of Mathematics for Programmers (2nd Edition) has sold 180,000 copies in total. By introducing the common mathematical knowledge in programming to programmers, we can cultivate the mathematical thinking of primary programmers. The second version also added machine learning and other content to solve the math pain points in the programming process of programmers.

Programmer mathematics 2: Probability Statistics covers random variables, Bayesian formulas, probability distributions of discrete and continuous values, covariance matrices, multivariate normal distributions, estimation and testing theory, pseudo-random numbers, and various applications of probability theory.

Programmer’s Mathematics 3: Linear Algebra includes vector, matrix, determinant, matrix inverse, linear equation, eigenvalue, diagonalization, Jordan standard form, eigenvalue algorithm, LU decomposition, etc.

3. Turing’s Mathematical Classics

An immortal mathematical classic

Basic Topology

Author: [English] mark Armstrong |, sun feng

A Course in Pure Mathematics (9th Edition)

Author: [English] Godfrey, hardy | translator: Zhang Mingyao

Inequalities (2nd Edition)

Author: [English] Godfrey, hardy, [British] John little wood, [the] George poly a | translator: the more people

Matrix Computation (4th Edition)

Author: Gene h.g. olub, Charles F.V an Loan | translator: xiao-liang cheng

Complex Analysis: A Visual Approach

Author: [us] Tristan Needham |, qi

“Basic Topology (revised edition)” is a classic introductory book of topology and a designated textbook of topology in foreign well-known universities. The author mainly introduces the topological invariants in topological space and the corresponding calculation methods. This book involves all kinds of methods and their applications in point set topology, geometric topology and algebraic topology, 139 diagrams and 350 thinking questions of different difficulties, cultivating the ability of geometric intuition. The content of this book is simple and easy, focusing on the combination of abstract theory and concrete application.

A Course in Pure Mathematics (9th Edition) is a century-old classic that laid the foundation for mathematical analysis courses in the early 20th century. In this book, the important content of the basic course of mathematical analysis — calculus is systematically elaborated, and the rigorous proof method is given for many classical mathematics, which is the crystallization of Hardy mathematics thought. In addition, the book collected a lot of exercises of extremely rich thinking value, what is worth mentioning is that, also collected in those days the Cambridge University of England honorary degree examination used test questions.

Inequalities (Second Edition), a classic work by Hardy, Littlewood, and Poria, discusses in detail some of the inequalities commonly used in analysis, It involves elementary mean value, average value of arbitrary function and convex function theory, various applications of calculus, infinite series, integral, some applications of variable integral, some theorems about bilinear form and multi-linear form, Hilbert inequality and its extension, etc.

Matrix Computing (4th Edition) is a classic work by Gene H. Golub, the late academician of the American Academy of Sciences and the American Academy of Engineering. It is a standard reference in the field of matrix computing. It systematically introduces the basic theories and methods of matrix computing, including: Matrix multiplication, matrix analysis, linear systems of equations, orthogonalization and least squares, eigenvalue problems, Lanczos method, matrix functions, seminars, etc.

Many of the algorithms in the book are available in software packages, with problem sets at the end of each section, notes and extensive references. The fourth edition adds about a quarter of the content, reflecting the rapid development of matrix computing in recent years.

Complex analysis: A Visual Approach is a book that has had a wide influence in the field of complex analysis. The author demonstrates various concepts, theorems and proof ideas with rich illustrations, which is very easy for readers to understand and fully reveals the mathematical beauty of complex analysis. The book covers complex functions as transformations, Mobius transformations, differential calculus, non-Euclidean geometry, circle numbers, complex integrals, Cauchy formulas, vector fields, harmonic functions, etc.

B. calculus

1. Introduction to Calculus (revised Edition)

 

Price: 99.00 yuan/page: 464

  • The winner of fields Prize, Wolf Prize, Japan Order of Culture, one of the “giants” of mathematics in the 20th century, Japanese mathematics master Bunhiko Xiaoping calculus masterpiece

  • A crisp, concise mathematical gem, a fluid, readable masterpiece of calculus

  • A New Calculus Theory combining Rigor and Intuition, Feeling the “Harmony” and “Aesthetic Feeling” of Mathematical Proof

Book for Japanese mathematician xiaoping bond of his life, he created a classic calculus book, is different from the general calculus textbooks, the authors focus on the mathematical analysis, combined with its own unique thinking and understanding, starting from the theory of real number of rigorous SiMou calculus, by guiding and inspire readers to think independently, enhance understanding understanding of calculus.

Simple calculus

 

Author: Masahiro Kanaga

Price: 49.00 yuan

  • Japanese popular “calculus introduction” reader

  • There is no need to memorize formulas, complicated calculations, just “read” to understand the principles of calculus

  • Rich illustrations and friendly explanations teach the “ingenious idea” of Japanese calculus introduction

Calculus is all about method. In short, if you grasp the “essentials” of thinking, you can easily understand complex equations. Introduction to calculus popular science books, the book to calculus “thinking method” as the core, popular life examples to explain the basic principle of calculus, formula derivation and practical application significance, to solve the calculus beginner encountered common confusion. This step-by-step, lively and intimate introduction to the principles of calculus is an “easy read” primer, with no cumbersome calculations or dry theories.

C. probability theory

1. Introduction to Probability (2nd edition · Revised Edition)

 

Dimitri P.Bertsekas, John N. Sitsiklis

Translator: Zheng Guozhong, Tong Xingwei

Isbn: 978-7-11 5-40507-4

Pricing: 79.00 YUAN/E-BOOK 39.99 yuan/Folio: 16 pages: 464

  • Academicians of the American Academy of Engineering, MIT and many other world famous textbooks

  • It is the first choice for science and engineering students to explain probability from an intuitive and natural perspective

  • A classic that strikes the perfect balance between brevity and rigor

This book is written on the basis of the introduction to Probability theory course offered by MIT. It is comprehensive in content, rich in examples and exercises, and has a strong structure that can meet the needs of different readers. This book introduces probability model, discrete random variable and continuous random variable, multivariate random variable, limit theory and other basic knowledge of probability theory. It also introduces advanced content such as moment generating function, modern definition of conditional probability, sum of independent random variable, least square estimation and so on.

2. Applying Stochastic Processes: Introduction to Probabilistic Models (11th edition)

 

By Sheldon M. Ross

Translator: Gong Guanglu

Isbn: 978-7-115-40430-5 (Chinese version)

978-7-115-38474-4 (English Version)

Pricing: 99.00 yuan/Folio: 16

Page 652 (Chinese version)

784 (English Version)

  • By internationally renowned statistician Sheldon M. Ross

  • Applied stochastic process classic textbook, actuarial science, artificial intelligence, machine learning essential reference

  • In the 11th edition, a large number of examples and exercises were added, and the contents of continuous time Markov chain and drift Brownian motion were revised to strengthen readers’ intuitive probability

Compared with other books on stochastic processes, this book is very practical. The main contents include random variable, conditional expectation, Markov chain, exponential distribution, Poisson process, stationary process, renewal theory and queuing theory, etc., and also include the application of stochastic process in physics, biology, operations research, network, genetics, economics, insurance, finance and reliability. Especially the content about stochastic simulation provides a powerful tool for the simulation calculation of stochastic system. The latest version also includes random wandering without left jump and the birth and death queuing model. There are about 700 problem sets in this book, with asterisks providing solutions.

This book has been adopted by university of California, Berkeley, Columbia University, Purdue University, University of Michigan, Oregon State University, University of Washington and many other well-known universities abroad.

3. Probability Theory and Its Applications (Volume 1• 3rd edition)

 

By William Feller

Translator: Hu Dihe

Isbn: 978-7-11 5-33667-5

Pricing: RMB 69.00 / page: 408

  • The best selling textbook on probability theory for 60 years

  • By William Feiler, the great probabilist

  • Translated by famous mathematician Hu Dihe

The book covers a wide range of topics, not only in discrete Spaces, but also in physics, chemistry, biology (especially genetics), game theory, and economics. The main contents include sample space and its probability calculation, random fluctuation of the sum of independent random variables, combination of events and conditional probability.

[D]

1. This is how Linear Algebra should be learned (3rd Edition)

 

By Sheldon Axler

Translator: Du Xiankun, Liu Dayan, Ma Jing

Isbn: 978-7-11 5-43178-3

Pricing: 49.00 YUAN/Folio: 16 pages / 268

  • Accepted as a classic exposition of linear algebra

  • The original version has been sold well in more than 30 countries and adopted as textbooks by more than 200 universities

  • Linear operators are described in terms of vector Spaces and linear mappings, instead of obscure determinants

  • Contains 561 problem sets and lots of examples

  • The third edition has been completely revised, most of the exercises have been replaced, product space, quotient space and duality have been added, and a chapter on operators on real vector Spaces has been completely rewritten

This book emphasizes abstract vector Spaces and linear mappings, covering polynomials, eigenvalues, eigenvectors, inner product Spaces, traces and determinants, etc. The content arrangement and processing method of this book is quite different from that of domestic common practice. It completely disregards determinant, and uses a more direct and simple method to elaborate the basic theory of vector space and linear operator.

Notes on terms, conclusions, mathematicians, proof ideas and Revelations add interest and enhance the reader’s understanding of concepts and methods of thought.

2. Matrix Calculation (English Version • 4th Edition)

 

Gene H.Golub, Charles F. Vanloan

Isbn: 978-7-11 5-34610-0

Pricing: 99.00 YUAN/Folio: 16 pages / 772

  • Numerical linear algebra computation field bible

  • Gene H. Golub, founder of modern matrix computing

  • The most authoritative and comprehensive book on numerical linear algebra in the world

  • The fourth edition is a new revision, adding about a quarter of the content, including tensor computation, fast transformation, parallel LU and other topics, reflecting the latest progress in matrix computing in recent years

This book systematically introduces the basic theory and method of matrix calculation. Topics include: matrix multiplication, matrix analysis, linear systems of equations, orthogonalization and least squares, eigenvalue problems, Lanczos methods, matrix functions, and seminars. Many of the algorithms in the book are available in software packages, with problem sets at the end of each section, notes and extensive references.

The book has been used as a course material or main reference book by many world-renowned universities such as University of California, Stanford University, University of Washington, University of Chicago, graduate School of Chinese Academy of Sciences and so on.

3. Matrix Analysis (English edition • 2nd Edition)

 

By Roger A. Horn, Charles R. Johnson

Isbn: 978-7-11 5-40569-2

Pricing: 99.00 YUAN/Folio: 16 pages / 660

  • Matrix theory classic works, international mainstream teaching materials

  • The authoritative tutorial and indispensable reference for matrix analysis theory

  • The second edition was completely revised and updated, with new sections covering singular values, CS decomposition, and Weyr normal forms, among other things, along with more than 1100 questions and exercises from the linear algebra course

This book describes the classical and modern methods of matrix analysis from the point of view of mathematical analysis. The main contents are: eigenvalue, eigenvector and similarity; Unitary similarity and unitary equivalence; Similarity standard form and trigonometric decomposition; Hermite matrix, symmetric matrix and unitary consistency; Vector norm and matrix norm; Estimation and perturbation of eigenvalues; Positive definite matrix and semi-positive definite matrix; Positive and non-negative matrices.

E. Mathematical analysis

1. Lecture Eight on Mathematical Analysis (revised Edition)

 

я : He is

Translator: Wang Huilin qi Minyou

Isbn: 978-7-11 5-39747-8

Pricing: 29.00 YUAN/Folio: 16 pages / 184 pages

  • With short length and easy to understand writing method for readers to clear up doubts, let you gain a lot

  • This short lecture will give you an overview of mathematical analysis and help you grasp the essence of mathematical analysis

  • By the famous Soviet mathematician, mathematics educator, Moscow probability school of the founder of the classic textbook

It is a clear and fascinating book that thoroughly reviews the main topics of mathematical analysis, including continuums, limits, functions, series, derivatives, integrals, series expansion of functions, and differential equations.

2. Tao Zhexuan’s Real Analysis (3rd edition)

 

Translator: Li Xin

Isbn: 978-7-11 5-48025-5

Pricing: 99.00 YUAN/Folio: 16 pages / 470

  • Amazon original 4.8-star review

  • From the teaching notes of Tao Zhexuan, a gifted Chinese mathematician and Fields Medal winner

This book mainly introduces some contents of mathematical analysis, starting with the construction of number system and set theory, gradually in-depth to series, functions and other advanced mathematical content, with detailed examples, exercises after each part of the content is closely related to the content of the text, which is conducive to readers to master the content. In the appendix, the book also introduces the basis of mathematical logic and decimal system, highlighting the rigor and foundation.

F. Mathematical statistics

1. Sparse statistical learning and its application

 

By Trevor Hastie, Robert Tibshirani and Martin Wainwright

Translator: Liu Bo, Jing Pengjie

Isbn: 978-7-11 5-47261-8

Pricing: 89.00 YUAN/Folio: 16 pages / 300

  • Statistical machine learning masters

  • The sparse statistical model and its research results are introduced comprehensively

  • Lasso model is used to solve hot issues such as big data mining and machine learning

Sparse statistical model has only a few non-zero parameters or weights, which embodies the concept of simplifying complexity, so it is widely used in many fields. This book summarizes the learning of sparsity statistics. Centering on lasso method, the book gradually includes other methods, and discusses the solution and application of many sparsity problems in depth. It not only includes a large number of examples and charts, but also includes literature notes and after-class exercises, which is an excellent reference for in-depth learning of statistical knowledge.

2. Core methods of statistics and their applications

By Simon N. Wood

Translator: Shi Liwei

Pricing: RMB 69.00 / pages: 216

  • Combine theory with numerical calculation

  • Simon N. Wood, professor of statistics at the University of Bath and author of the R Baumgcy, is a well-written reference book on statistics for those with a mathematical foundation

  • Covers the core knowledge required to understand and apply parametric statistical methods to build new methods for data analysis

This book mainly introduces the problems in statistical model and statistical inference, and introduces maximum likelihood method and Bayesian method to solve these problems. Overview of R language; The large sample theory of maximum likelihood estimation is briefly introduced, and then the numerical methods involved in applying the theory are discussed. The numerical method for Bayesian computation — Markov chain Monte Carlo method is described. The theory and application of linear models are introduced.

G. Computer mathematics

1. Concrete Mathematics: Fundamentals of Computer Science (2nd edition)

Ronald L.Graham, Donald E.Knuth, Oren Patashnik

Translator: Zhang Mingyao, Zhang Fan

Isbn: 978-7-11 5-30810-8

Pricing: 99.00 YUAN/Folio: 16 pages / 580

  • It scored 9.4 out of 10 on Douban

  • The classic book co-authored by a top mathematician and computer scientist has been adopted as a textbook by many prestigious universities around the world

  • Not only about mathematical problems and techniques, but also about problem-solving

  • It includes more than 500 exercises in six categories, and provides all the answers to help readers deepen their understanding of the contents of the book

  • Some plain, some profound, some serious, or humorous graffiti, let you experience the beauty of mathematics in a relaxed and happy state of mind

This book explains many mathematical knowledge and techniques used in computer science. It teaches you how to evolve a practical problem into a mathematical model step by step and then solve it by computer, with special emphasis on algorithm analysis. Its main content involves sum, integral function, number theory, binomial coefficient, special number, generating function, discrete probability, asymptotic formula and so on, which are necessary knowledge for programming.

2. Vernacular Machine learning mathematics

 

Author: Tashi Xiengo

Translator: Zheng Mingzhi

A book to master the basic mathematics of machine learning

1. Step by step guidance, easy to understand the form of dialogue 2. Implement classification and regression algorithms in Python

This book introduces the practical mathematical basics of machine learning through a dialogue between Ayanami, a programmer who is learning machine learning, and her friend Miso, combined with specific problems of regression and classification. It focuses on math formulas and symbols that can easily become obstacles to learning. At the same time, the application of mathematical formulas is explained through practical Python programming to deepen the readers’ understanding of relevant mathematical knowledge.

The mathematics of deep learning

 

Authors: Yoshiyuki Inai, Tatsumi Inai

Translator: Yang Ruilong

  • Combines 235 illustrations and plenty of examples

  • Based on Excel practice, straight to the fundamental principle of neural network

Based on rich illustrations and concrete examples, the book introduces the basic mathematical knowledge related to deep learning in a popular way. Chapter 1 introduces the general situation of neural network. Chapter 2 introduces the mathematical basics needed to understand neural networks. Chapter 3 introduces the optimization of neural networks. Chapter 4 introduces neural network and error back propagation method. Chapter 5 introduces deep learning and convolutional neural networks.

4. Practical statistics for data scientists

 

By Peter Bruce and Andrew Bruce

Translator: Galle

Price: 89.00 yuan

  • Douban score 9.1

  • “Data Warehouse” top seller list

  • Systematically sort out important statistical concepts and demonstrate the specific application of statistical methods

The book explains the crucial statistical concepts in data science and shows how various statistical methods can be applied to data science. The authors introduce key concepts related to data science in statistics in a way that is easy to understand, browse, and refer to. The importance and usefulness of statistical concepts in data science are explained, and the reasons are given.

5. The mathematics and physics of game development

 

Author: Jie Kato

Translator: Xu Qian

  • Here’s the secret to making your game feel real and flowing

  • 42 programming examples, through the game development of the governor of the two arteries

  • 134 illustrations, clear explanation of game programming five basic implementation

A rigorous selection of the most commonly used mathematical and physical knowledge in game development, illustrated through game development examples, in order from easy to hard. Chapter 1 to Chapter 5 respectively explain the movement of objects, rolling, collision detection, the production of light, and the subdivision processing of picture switching. These five chapters cover everything you need to know about 2D games, with a small selection of the basics of 3D game programming. Chapter 6 takes a systematic look at the mathematics and physics of game development to help readers understand the first five chapters.

H. the him

1. Financial Time Series Analysis (3rd Edition)

 

By Ruey S. Say

Translator: Wang Yuanlin, Wang Hui, Pan Jiazhu

Isbn: 978-7-11 5-28762-5

Pricing: RMB 85.00/540 pages

  • A rare masterpiece in financial time series analysis

  • This edition not only updates the data used in the previous edition, but also provides R commands and examples, making it a cornerstone for understanding important statistical methods and techniques

This book comprehensively expounds financial time series, and mainly introduces the current research hotspots and some latest research results of financial time series theory and methods, especially value at risk calculation, high-frequency data analysis, stochastic volatility modeling and Markov chain Monte Carlo method. In addition, the book also systematically describes financial econometric models and their applications in financial time series data and modeling. All models and methods are based on actual financial data, and the commands of the computer software used are given.

2. Xiaobo speaks 10

 

Ingrid Daubechies

Isbn: 978-7-11 5-43898-0

Pricing: 79.00 YUAN/Folio: 16 pages / 356 pages

  • An important contributor to wavelet theory, the latest Chinese translation of mathematician classics

  • Recognized as a classic work in mathematics, it contains the most advanced results of wavelet analysis in the world since the 1980s

  • Introduction to wavelet analysis must read

This book comprehensively discusses the main principles and methods of wavelet analysis, and gives a large number of practical examples, describes many applications of wavelet. This book is suitable for researchers in engineering mathematics, signal analysis, communication and other fields as well as teachers and students of relevant majors in colleges and universities.