Programmer's mathematics (a mathematical book written for programmers and Friends) (China-pub)

Programmer's mathematics
Basic Information
Author: (day) jiechenghao [Translator's introduction]
Translator: Guan Jie
Series name: Turing programming Series
Press: People's post and telecommunications Press
ISBN: 9787115293688
Mounting time:
Published on: February 1, November 2012
Start: 16
Page number: 232
Version: 1-1
Category: Computer> Computer science theory and basic knowledge> computing theory> comprehensive
Computer> Software and Program Design

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Introduction
Books
Computer books
Programmer's mathematics introduces common mathematical knowledge in programming for programmers, so as to cultivate the mathematical thinking of junior programmers. Readers do not need to be proficient in programming or mathematics. They only need to have four basic operations and multiplication methods to read this book.
The programmer's mathematics explains many mathematical methods closely related to programming, such as binary notation, logic, remainder, Permutation and combination, recursion, exponential explosion, and unsolvable problems, this paper analyzes classic problems and algorithms such as the seven bridges, Gaussian summation method, Tower of Hanoi, And the Fibonacci series. Guides readers to deeply understand the mathematical methods and ideas in programming.
"Programmer's mathematics" is suitable for programmers and programming and mathematics enthusiasts to read.
Programming is based on computer science, while computer science is based on mathematics. Therefore, learning mathematics helps to consolidate the foundation of programming and write more robust programs.
Programmer's mathematics introduces common mathematical knowledge in programming for programmers, so as to cultivate the mathematical thinking of junior programmers. Readers do not need to be proficient in programming or mathematics. They only need to have four basic operations and multiplication methods to read this book.
The programmer's mathematics explains many mathematical methods closely related to programming, such as binary notation, logic, remainder, Permutation and combination, recursion, exponential explosion, and unsolvable problems, this paper analyzes classic problems and algorithms such as the seven bridges in gonisburg, the juvenile Gaussian summation method, the Tower of Hanoi, And the Fibonacci series. Guides readers to deeply understand the mathematical methods and ideas in programming.
The division of labor between programmers and computers is also discussed in mathematics of programmers. After reading this book, you will have a deeper understanding of man-machine cooperation based on programs.

Directory
Programmer's mathematics
Chapter 1 0 0 stories -- none is
Content of this Chapter
Memories of first-year primary school
10-digit notation
What is decimal notation?
Decomposition 2503
Binary Notation
What is binary notation?
Decomposition 1100
Base Conversion
Why is the binary notation used in the computer?
Count by bit
What is bitwise notation?
Do not use the number of Roman in the bitwise notation
Exponential law
What is the power 0 of 10?
What is 10-1?
Rule Extension
Think about 20
What is 2-1?
0
0: placeholder
0: unify standards and simplify rules
0 in daily life
The discovery of human limitations and structures
Review historical processes
To surpass the limits of mankind
Summary of this Chapter
Chapter 2 logic-the dual world of truth and false
Content of this Chapter
Why is logic so important?
Logic is a tool for eliminating ambiguity
Readers who disagree with the logic
Fare-both integrity and exclusiveness
Fare rules
True and false
Are there any "Omissions"
Are there any "duplicates"
Draw a digital axis
Note the Boundary Value
Integrity and exclusivity
If statement Decomposition
The logic is basically two branches
Create complex propositions
Logical non-
Logic and -- A and B
Logic or -- A or B
XOR -- A or B (but not all)
Equal -- A and B are equal
Implication -- if A is, B
Are all included?
De Morgan's Law
What is d Morgan's law?
Parity
Karnotu
2-light game
First, use the logical expression for consideration.
Learn how to use kanotu
Three-light game
Contains undefined Logic
Conditional logic and (&&)
Conditional logic or (ii)
Negative in the Three-value Logic (!)
De Morgan's law of Three-value Logic
Are all included?
Summary of this Chapter
Chapter 1 remainder-periodicity and grouping
Content of this Chapter
Questions about the number of weeks (1)
Thinking questions (the day of the week after 100 days)
Questions and answers
Using Remainder
The power of the remainder-groups large numbers once
Questions about the number of weeks (2)
Thinking questions (the day of the week after 10100 days)
Tip: Can I calculate it directly?
Questions and answers
Discovery rules
Intuitively grasp rules
Questions about multiplication
Questions (1234567987654321)
Tip: use trial calculation to find out the rule
Questions and answers
Review: relationship between law and remainder
Communication through black and white games
Questions
Prompt
Questions and answers
Parity
The parity bit divides the number into two sets.
Search for questions About lovers
Questions (looking for lovers)
Tip: Calculate a small number first
Questions and answers
Review
Questions about building a straw mat
Thinking questions (laying a straw mat in the Room)
Tip: calculate the number of mats first
Questions and answers
Review
One stroke thinking questions
Questions (seven bridges in gonisburg)
Tip: Try to calculate
Tip: simplify it.
Tip: considering population and export
Questions and answers
Parity
Summary of this Chapter
Chapter 2 mathematical induction-how to conquer Infinite Series
Content of this Chapter
Gaussian summation
Thinking questions (save the money in the piggy bank)
Think about it
Xiao Gaussian's answer
Let's discuss the answer to Mr. Gauss.
Induction
Mathematical induction -- how to conquer Infinite Series
Assertions of integers greater than 0
Gaussian assertions
What is mathematical induction?
Try to conquer Infinite Series
Use mathematical induction to prove Gaussian's assertions
Finding the sum of odd numbers -- An Example of mathematical induction
Odd sum
Mathematical induction
Graphical description
Incorrect mathematical induction
Question (color of black and white pawns)
Tip: do not confuse the image
Questions and answers
Programming and mathematical induction
Mathematical induction represented by Loops
Cycle unchanged
Summary of this Chapter
Chapter 4 arrangement and combination-a solution to the counting problem
Content of this Chapter
Count -- correspondence with Integers
What is Count
Note "omission" and "repetition"
Tree planting problem-do not forget 0
Questions about Tree Planting
Addition Law
Addition Law
Multiplication Law
Multiplication Law
Replacement
Replacement
To sum up
Thinking questions (playing cards)
Arrange
Arrange
To sum up
Tree Structure-can you recognize the essence?
Combination
Combination
To sum up
Relationship of replacement, arrangement, and combination
Questions and exercises
Repeated combination
Be good at using logic
Summary of this Chapter
Chapter 2 recursion-define yourself
Content of this Chapter
Tower of Hanoi
Questions (piata)
Tip: Start With qingta
Questions and answers
Analytic Expression
Program for solving tower of Hanoi
Find the recursive structure
Next step
Recurrence definition of factorial
Thinking questions (and definitions)
Recursion and induction
Fibonacci Series
Thinking questions (continuously breeding animals)
Fibonacci Series
Pascal triangle
What is Pascal triangle?
Recursively define the number of combinations
Mathematical Theory of a combination
Recursive graphics
Draw a tree in Recursion
Actual plot
Sherpinski triangle
Summary of this Chapter
Chapter 4 Exponential Explosion-how to solve complex problems
Content of this Chapter
What is exponential explosion?
Questions (origami)
Exponential Explosion
Multiple games-difficulties caused by exponential explosion
Program setting options
You cannot think of it as "Limited ".
Binary Search-search by exponential explosion
Search for questions about prisoners
Tip: first think about the small number of people
Questions and answers
Find the recursive structure and Recurrence Formula
Binary Search and Exponential Explosion
Logarithm-A Tool for mastering Exponential Explosion
What is logarithm
Relationship between logarithm and multiplication
Base 2 logarithm
Base-2 logarithm exercises
Logarithm chart
Exponential law and logarithm
Logarithm and calculation ruler
Password-exponential explosion Encryption
Brute force cracking
Relationship between wordlength and security
How to deal with Exponential Explosion
Understand the size of the problem space
Four Solutions
Summary of this Chapter
Chapter 4 unsolvable problems-Number of unsolvable programs
Content of this Chapter
Reverse Identification Method
What is anti-Evidence
Questions
Counterproof method considerations
Count
What is a handful
Example of a count-and-number set
Is there an unmeasurable set?
Diagonal argument
The set of All Integer series is unmeasurable.
The set of all real numbers is unmeasurable.
The set of all functions is also unmeasurable.
Unsolved problem
What is unsolved
Unsolved Problems
Questions
Downtime Problems
Shutdown
Processing Program
What is a shutdown problem?
Proof of downtime
For readers who have not yet understood
There are many unsolved problems
Summary of this Chapter
Chapter 2 What is a programmer's mathematics -- Summary
Content of this Chapter
What is problem solving?
Recognize patterns and abstract them
The wisdom that is not good at giving birth
Fantasy Law
Programmer's mathematics

Source of this book: China Interactive publishing network