Math optimization made easy with comics
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Description
Book Introduction
If you know the maximum and minimum values of a function, you can easily maximize your company's profits or minimize its losses!
Math optimization made easy with comics
This book allows readers to naturally understand the meaning of optimization formulas (mathematical symbols, calculation formulas, etc.) while watching the cartoon story, and learn practical application through specific examples.
Everyone has probably learned about the maximum and minimum of functions in middle and high school mathematics.
Through this, we know that it is good to maximize profits and minimize losses, and this is optimization.
Optimization is taught in college as a discipline called management science.
The math level starts with the assumption that you know linear algebra, which you learn in the first year of college.
However, if you can only conjure up images of maximum and minimum, you can perform optimization without understanding the complex calculations at all.
This book first provides an overview through comics, and the main text that supplements the comics provides practical examples with minimal formulas, helping readers avoid the perception that they are unfamiliar with mathematical optimization.
Recently, many people have been creating programs for simple mathematical optimization using Python. If you read this book first, you will be able to perform optimization using Python much more flexibly.
Math optimization made easy with comics
This book allows readers to naturally understand the meaning of optimization formulas (mathematical symbols, calculation formulas, etc.) while watching the cartoon story, and learn practical application through specific examples.
Everyone has probably learned about the maximum and minimum of functions in middle and high school mathematics.
Through this, we know that it is good to maximize profits and minimize losses, and this is optimization.
Optimization is taught in college as a discipline called management science.
The math level starts with the assumption that you know linear algebra, which you learn in the first year of college.
However, if you can only conjure up images of maximum and minimum, you can perform optimization without understanding the complex calculations at all.
This book first provides an overview through comics, and the main text that supplements the comics provides practical examples with minimal formulas, helping readers avoid the perception that they are unfamiliar with mathematical optimization.
Recently, many people have been creating programs for simple mathematical optimization using Python. If you read this book first, you will be able to perform optimization using Python much more flexibly.
- You can preview some of the book's contents.
Preview
index
preface
Prologue: Weekend Late-Night Part-Time Jobs and Monday First-Period Lectures
Chapter 1: What is Repair Optimization?
1-1 'Maximum' and 'Minimum' are optimal
Let's express the real-world problem simply.
The formula is a set of 3
The feeling of satisfaction can also be quantified.
There are many different types of optimization problems.
Get familiar with the graph of a function
Graphs are a great support!
1-2 This is enough math for optimization.
How can vectors and matrices help?
Scalar, vector, matrix
Let's understand the characteristics of vectors through pictures.
Notation method
A system of linear equations can be expressed as the product of a matrix and a vector.
How can differentiation and gradient help?
How can the gradient vector help?
Let's use differentiation
Formula for slope (slope vector)
Slope and gradient
Let's differentiate it twice, Hessian matrix
Chapter 2 Linear Programming Problems
2-1 Example of a linear programming problem
I want to produce so that I can make the most profit!
The seasoning problem has also been formalized
Executable region and objective function
To tackle complex, large-scale problems
2-2 Group law and internal law
Images of two solution methods
What is the algorithm (calculation) for group law?
2-3 Dual Theory
Let's understand the image of a twin
It can be easily solved thanks to the dual problem
What is the dual problem of the seasoning problem?
Chapter 3 Nonlinear Programming Problems
3-1 Example of a Nonlinear Plan
Linear and nonlinear in three-dimensional space
Let's predict the number of beer orders
Minimize errors
Even complex functions can be predicted.
Nonlinear programming problems may or may not have constraints.
3-2 Optimality Conditions
Global optimum and local optimum
First, let's find the stop.
How to find a stop
Convex sets and convex functions
3-3 repetition method
Renewal of the year
Direct and iterative methods
Renewal formula of the iterative method
In the case of maximization, climbing
Global convergence and local convergence
How to choose a navigation direction
Chapter 4 Integer Programming Problems and Combinatorial Optimization Problems
4-1 Examples of integer programming and combinatorial optimization problems
Constraint called integer
What is a combination structure?
For efficient patrolling
Backpack problem
Problems with 0-1 constraints
4-2 Approximate and exact solutions
There are two ways to solve it.
What are approximate and exact solutions?
Greed Law (Law of the Greedy)
Branching limitation
Epilogue
supplement
For further study
Search
Prologue: Weekend Late-Night Part-Time Jobs and Monday First-Period Lectures
Chapter 1: What is Repair Optimization?
1-1 'Maximum' and 'Minimum' are optimal
Let's express the real-world problem simply.
The formula is a set of 3
The feeling of satisfaction can also be quantified.
There are many different types of optimization problems.
Get familiar with the graph of a function
Graphs are a great support!
1-2 This is enough math for optimization.
How can vectors and matrices help?
Scalar, vector, matrix
Let's understand the characteristics of vectors through pictures.
Notation method
A system of linear equations can be expressed as the product of a matrix and a vector.
How can differentiation and gradient help?
How can the gradient vector help?
Let's use differentiation
Formula for slope (slope vector)
Slope and gradient
Let's differentiate it twice, Hessian matrix
Chapter 2 Linear Programming Problems
2-1 Example of a linear programming problem
I want to produce so that I can make the most profit!
The seasoning problem has also been formalized
Executable region and objective function
To tackle complex, large-scale problems
2-2 Group law and internal law
Images of two solution methods
What is the algorithm (calculation) for group law?
2-3 Dual Theory
Let's understand the image of a twin
It can be easily solved thanks to the dual problem
What is the dual problem of the seasoning problem?
Chapter 3 Nonlinear Programming Problems
3-1 Example of a Nonlinear Plan
Linear and nonlinear in three-dimensional space
Let's predict the number of beer orders
Minimize errors
Even complex functions can be predicted.
Nonlinear programming problems may or may not have constraints.
3-2 Optimality Conditions
Global optimum and local optimum
First, let's find the stop.
How to find a stop
Convex sets and convex functions
3-3 repetition method
Renewal of the year
Direct and iterative methods
Renewal formula of the iterative method
In the case of maximization, climbing
Global convergence and local convergence
How to choose a navigation direction
Chapter 4 Integer Programming Problems and Combinatorial Optimization Problems
4-1 Examples of integer programming and combinatorial optimization problems
Constraint called integer
What is a combination structure?
For efficient patrolling
Backpack problem
Problems with 0-1 constraints
4-2 Approximate and exact solutions
There are two ways to solve it.
What are approximate and exact solutions?
Greed Law (Law of the Greedy)
Branching limitation
Epilogue
supplement
For further study
Search
Publisher's Review
Target audience
ㆍStudents in departments or faculties of information, economics, and business administration
ㆍStudents in the Department of Data Science who can take the exam without taking mathematics
Students weak in management science and OR (operations and research)
ㆍEngineer SE, etc. who deals with maximizing the effectiveness of policies (maximum) and reducing costs (minimum)
ㆍStudents in departments or faculties of information, economics, and business administration
ㆍStudents in the Department of Data Science who can take the exam without taking mathematics
Students weak in management science and OR (operations and research)
ㆍEngineer SE, etc. who deals with maximizing the effectiveness of policies (maximum) and reducing costs (minimum)
GOODS SPECIFICS
- Date of issue: January 15, 2025
- Page count, weight, size: 208 pages | 182*235*20mm
- ISBN13: 9788931574579
- ISBN 10: 8931574576
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