Math Teaching \ 1-1
This book can be used as a textbook in the "Analytical Geometry" courses taught in the first (or second) grades of the mathematics and mathematics teaching departments of universities.
In addition to covering the basic subjects that the students studying in these departments will need in the lessons they will study in the advanced classes, it will also help them in the subjects that the prospective teachers will teach while teaching in high schools. These topics are given quite concisely without going into too much detail. The connections between the subjects were fully established and care was taken not to leave any open questions.
After each concept, enough examples are given to explain this concept. A sufficient number of exercises are included at the end of each section to make the subject comprehend. Solutions to all of these exercises have been published as a separate book.
The problems are ordered from easy to difficult, and abstract problems are placed at the end. The problems included in the book are not very specific problems in this field, but rather the type of questions that will be easily understood by the students, will make the students love the Analytical Geometry course and will better understand and reinforce the analytical geometry knowledge that will form the basis of the courses they will read in the advanced grades. The results of the problems and the actions to be taken while obtaining these results have been chosen in a way that will not tire the reader.
In addition to covering the basic subjects that the students studying in these departments will need in the lessons they will study in the advanced classes, it will also help them in the subjects that the prospective teachers will teach while teaching in high schools. These topics are given quite concisely without going into too much detail. The connections between the subjects were fully established and care was taken not to leave any open questions.
After each concept, enough examples are given to explain this concept. A sufficient number of exercises are included at the end of each section to make the subject comprehend. Solutions to all of these exercises have been published as a separate book.
The problems are ordered from easy to difficult, and abstract problems are placed at the end. The problems included in the book are not very specific problems in this field, but rather the type of questions that will be easily understood by the students, will make the students love the Analytical Geometry course and will better understand and reinforce the analytical geometry knowledge that will form the basis of the courses they will read in the advanced grades. The results of the problems and the actions to be taken while obtaining these results have been chosen in a way that will not tire the reader.
Numerical analysis (numerical analysis) consists of methods used to find approximate solutions for problems that cannot be solved analytically or which are very difficult to solve. In recent years, the use of numerical analysis methods has increased in parallel with the developments in the field of computers. Numerical analysis methods are frequently used in many engineering fields and applied sciences.
In this book, numerical analysis methods and their MATLAB applications are explained.
The book consists of ten main chapters:
In the first chapter, the history of numerical analysis, the basic theorems used, machine numbers and errors are included. In the second part, direct and iterative solution methods for linear equation systems are mentioned. In the third chapter, solution methods for nonlinear equations and systems of nonlinear equations are covered. In the fourth chapter, the theory and applications of interpolation and polynomial approaches are given. In the fifth chapter, the subjects of curve fitting, least squares method, curve fitting with orthogonal polynomials, approximation with trigonometric functions are given. In the sixth chapter, numerical derivative formulas used to find the approximate derivative value are discussed. In the seventh chapter, numerical integral methods are covered to find the approximate integral value. In addition, improper integrals and multiple integrals are also included. In the eighth chapter, one-step and multi-step solution methods for ordinary differential equations and systems of ordinary differential equations are given. In addition, boundary value problems are also discussed. In the ninth chapter, the finite difference method used for numerical solutions of partial differential equations is covered. Finite difference method for Laplace equation, heat equation and wave equation is explained. In the last chapter, MATLAB applications of all numerical methods described in the book are discussed. This section contains all the MATLAB functions and MATLAB codes used. At the end of each chapter, there are exercises and answers related to the topic.
This book is a useful resource for all engineering students using undergraduate and graduate level mathematics, applied mathematics, and numerical analysis.
In this book, numerical analysis methods and their MATLAB applications are explained.
The book consists of ten main chapters:
In the first chapter, the history of numerical analysis, the basic theorems used, machine numbers and errors are included. In the second part, direct and iterative solution methods for linear equation systems are mentioned. In the third chapter, solution methods for nonlinear equations and systems of nonlinear equations are covered. In the fourth chapter, the theory and applications of interpolation and polynomial approaches are given. In the fifth chapter, the subjects of curve fitting, least squares method, curve fitting with orthogonal polynomials, approximation with trigonometric functions are given. In the sixth chapter, numerical derivative formulas used to find the approximate derivative value are discussed. In the seventh chapter, numerical integral methods are covered to find the approximate integral value. In addition, improper integrals and multiple integrals are also included. In the eighth chapter, one-step and multi-step solution methods for ordinary differential equations and systems of ordinary differential equations are given. In addition, boundary value problems are also discussed. In the ninth chapter, the finite difference method used for numerical solutions of partial differential equations is covered. Finite difference method for Laplace equation, heat equation and wave equation is explained. In the last chapter, MATLAB applications of all numerical methods described in the book are discussed. This section contains all the MATLAB functions and MATLAB codes used. At the end of each chapter, there are exercises and answers related to the topic.
This book is a useful resource for all engineering students using undergraduate and graduate level mathematics, applied mathematics, and numerical analysis.
Once Upon a Time Geometry is a book that tells the 2500-year history of geometry through breaking points. The most important reason for the difficulties that mathematics students face while learning pure mathematics is that they cannot establish the necessary relationship between the mathematical formulas they learn and the world they live in. Likewise, philosophy students have close thoughts about mathematics and the history of mathematics. First of all, what is wanted to be done with this book is to establish the relationship between philosophy and the history of mathematics through geometry as clearly as possible. Secondly, it is to give an idea about the position of geometry in mathematics and philosophy of mathematics.
Since Euclid's "Elements," geometry has been in a position to promise much more than ground measurement. It is about the objects that are at the center of man's understanding of himself and the universe he lives in.
The main reason for this is that geometry, besides being a type of knowledge produced by the human mind, serves as a key to understanding the universe.
Since Euclid's "Elements," geometry has been in a position to promise much more than ground measurement. It is about the objects that are at the center of man's understanding of himself and the universe he lives in.
The main reason for this is that geometry, besides being a type of knowledge produced by the human mind, serves as a key to understanding the universe.
This book contains solutions to exercises from the author's book “Analytical Geometry”. It is prepared for the benefit of our students in the Analytical Geometry courses taught in the first (or second) grades of universities.
The problems in this book will not only cover the topics that our students will need in the lessons they will study in the advanced grades, but also will help them in the topics that prospective teachers will teach while teaching in high schools. If the solutions of the exercises are included in the "Analytical Geometry" book, it was thought that it would be more appropriate to collect it in a separate book, since the volume of the book would increase a lot.
The problems are ordered from easy to difficult, and abstract problems are placed at the end. The problems included in the book are not very specific problems in this field, but rather the type of questions that can be easily understood by the students, that will make them love the Analytical Geometry course and that will provide a basis for the courses they will read in the advanced classes, and will better understand and reinforce their knowledge of Analytical Geometry. The problems, results and the actions to be taken while obtaining these results have been chosen in a way that will not tire the reader.
The problems in this book will not only cover the topics that our students will need in the lessons they will study in the advanced grades, but also will help them in the topics that prospective teachers will teach while teaching in high schools. If the solutions of the exercises are included in the "Analytical Geometry" book, it was thought that it would be more appropriate to collect it in a separate book, since the volume of the book would increase a lot.
The problems are ordered from easy to difficult, and abstract problems are placed at the end. The problems included in the book are not very specific problems in this field, but rather the type of questions that can be easily understood by the students, that will make them love the Analytical Geometry course and that will provide a basis for the courses they will read in the advanced classes, and will better understand and reinforce their knowledge of Analytical Geometry. The problems, results and the actions to be taken while obtaining these results have been chosen in a way that will not tire the reader.
Differential Equations is one of the cornerstones of modern mathematics and, together with Linear Algebra, is a necessary discipline for solving many problems in engineering, natural sciences, economics, physical and social sciences. R&D studies on computer technologies have revealed new techniques for the solution of differential equations. In this way, it became possible to solve the problems modeled with Differential Equation Systems.
This book has been prepared to be taught in the Differential Equations course in the Academic Program of Universities. Book; In addition to the information that forms the basis of Differential Equations, it also includes the topics related to the applications in the field courses taught in the Academic Program of Engineering.
Book; It consists of the titles of First Order Differential Equations, Applications of First Order Differential Equations, Higher Order Linear Differential Equations, Laplace Transform, Applications of Second Order Differential Equations and Linear Differential Equations with Variable Coefficients.
This book has been prepared to be taught in the Differential Equations course in the Academic Program of Universities. Book; In addition to the information that forms the basis of Differential Equations, it also includes the topics related to the applications in the field courses taught in the Academic Program of Engineering.
Book; It consists of the titles of First Order Differential Equations, Applications of First Order Differential Equations, Higher Order Linear Differential Equations, Laplace Transform, Applications of Second Order Differential Equations and Linear Differential Equations with Variable Coefficients.
This book was created by blending the lecture notes used for years for the Differential Equations course taught in the Department of Mathematics, Faculty of Science, Ankara University, with the current literature, and rearranging them in the required width and depth in an original way. Consisting of fifteen chapters and 554 pages, this book is designed to be taught in undergraduate mathematics programs for two semesters.
In this book, basic concepts, theorems and solution methods, which are indispensable for differential equations, are emphasized and attention is drawn to the real-life application areas of differential equations. Graphs were drawn, tables were set up, sufficient number of examples were solved and many exercises were given so that the concepts, theorems and solution methods covered could be easily understood. In addition, sample problems for different application areas of differential equations were examined and a series of exercises were prepared in this context. Finally, the answers to most of the exercises left to the reader are shared at the end of the book for self-control. In this respect, this book has general norms that can be followed and taught as a textbook not only in mathematics departments, but also in physics, astronomy and space sciences and engineering departments. In summary, anyone who has undergraduate or graduate education in basic sciences, engineering, economics and health and needs differential equations can easily benefit from this book as much as they want.
In this book, basic concepts, theorems and solution methods, which are indispensable for differential equations, are emphasized and attention is drawn to the real-life application areas of differential equations. Graphs were drawn, tables were set up, sufficient number of examples were solved and many exercises were given so that the concepts, theorems and solution methods covered could be easily understood. In addition, sample problems for different application areas of differential equations were examined and a series of exercises were prepared in this context. Finally, the answers to most of the exercises left to the reader are shared at the end of the book for self-control. In this respect, this book has general norms that can be followed and taught as a textbook not only in mathematics departments, but also in physics, astronomy and space sciences and engineering departments. In summary, anyone who has undergraduate or graduate education in basic sciences, engineering, economics and health and needs differential equations can easily benefit from this book as much as they want.
The General Mathematics book has been prepared for the courses given under the names such as Mathematics, General Mathematics, and Higher Mathematics, apart from the Mathematics Departments of the Faculties of Science and Letters. The study, which has a suitable content for the Mathematics curriculum given in the Economics and Economics Departments as well as the Technical Education Faculties and Education Faculties, has been written in an understandable style so that the students can learn the subjects better.
In the study, in which definitions, theorems and results are given in very simple terms, enough examples are solved and real numbers, functions, limit and continuity, derivative, integral, matrix, sequences and series are covered comprehensively.
In the study, in which definitions, theorems and results are given in very simple terms, enough examples are solved and real numbers, functions, limit and continuity, derivative, integral, matrix, sequences and series are covered comprehensively.
Ring Theory is a theory that is taught in the undergraduate courses of our universities and contains the basic tools of algebraic geometry in general. Its main motivation is to be able to do arithmetic with integers in new ring classes. In this respect, it relies entirely on the ability to think abstractly. Naming things and establishing relationships between them is the starting point of this process. The possibilities these new structures offer us are quite surprising.
In this book, we tried to present the first seven chapters taught at the undergraduate level in as much detail as possible, with clear proofs and solved questions. Secondly, we have written the last four chapters for undergraduate and graduate students who want to do research on these topics. Our main goal is to get them to the level where they can read articles on this subject.
We hope that the reader will develop reasoning skills and acquire the habit of proving by trying to solve the solved questions and the end-of-chapter questions.
Hope the book will be useful to all readers...
In this book, we tried to present the first seven chapters taught at the undergraduate level in as much detail as possible, with clear proofs and solved questions. Secondly, we have written the last four chapters for undergraduate and graduate students who want to do research on these topics. Our main goal is to get them to the level where they can read articles on this subject.
We hope that the reader will develop reasoning skills and acquire the habit of proving by trying to solve the solved questions and the end-of-chapter questions.
Hope the book will be useful to all readers...
This course book has been prepared on the basis of the content of the courses taught under the name of Statistics, General Statistics and Introduction to Statistics in Education Faculties, Science and Literature Faculties and Vocational Schools (Health Vocational Schools).
In the first chapter, the concepts of statistics and graphics, series and frequency curves are emphasized. In the next chapters, probability and probability function, expected values and moments, distribution theory, correlation and regression are studied with extensive examples.
In the first chapter, the concepts of statistics and graphics, series and frequency curves are emphasized. In the next chapters, probability and probability function, expected values and moments, distribution theory, correlation and regression are studied with extensive examples.
This book, which is the first of two volumes prepared for the general mathematics courses taught in the Business Administration and Economics Departments of our universities, has plenty of questions with solutions at the end of each section. The solution to each problem is explained broadly and clearly. Even if proofs of some theorems are not given while the subjects are being treated, it has been tried to geometrically imply why they are so. Most of the theorems and fundamental formulas have been proved.
There are enough examples in the book to explain the theorems and basic information. While introducing a new concept, the relation of this concept with previous concepts was established, and it was tried for our students to learn by understanding that information in the easiest way.
There are enough examples in the book to explain the theorems and basic information. While introducing a new concept, the relation of this concept with previous concepts was established, and it was tried for our students to learn by understanding that information in the easiest way.
This book, which is the second of two volumes prepared for the general mathematics courses taught in the Business Administration and Economics departments of our universities, has plenty of questions at the end of each section. The solution to each problem is explained broadly and clearly. Even if proofs of some theorems are not given while the subjects are being studied, it has been tried to intuit why this is the case. Some of the theorems and basic formulas have been proved.
There are enough examples in the book to explain the theorems and basic information. While introducing a new concept, the relation of this concept with previous concepts was established, and it was tried for our students to learn by understanding that information in the easiest way.
There are enough examples in the book to explain the theorems and basic information. While introducing a new concept, the relation of this concept with previous concepts was established, and it was tried for our students to learn by understanding that information in the easiest way.
From the micro level to the macro level, there is a dynamic order in life and the universe, even if it seems chaotic, and mathematics is an important tool in analyzing and expressing this order. The mathematical information revealed by the branches of science explaining nature and the universe and the information revealed by mathematics itself are in harmony within and between themselves. In short, where there is order of any kind, there is also mathematics.
Basic knowledge and skills that should be used in daily life such as measuring (number, length, area, volume, time) and calculating (shopping, determining the requirements for the completion of a job, sharing, finding direction, determining relationships, etc.) mark the emergence of mathematics. motivated. Therefore, before mathematical concepts and operations were defined, they were felt in life and the mental infrastructure of discovery was formed. When we consider numbers, shapes and properties, solving real life problems with a mathematical potential, and generally being able to reveal the solution methods to problems, as a mathematical thinking skill; It would be appropriate to define mathematics as an art of thinking. These basic elements have gradually diversified and progressed with the tendency of the mind to develop them, the desire to know and understand, the development of life in a way that will increase the use of mathematical knowledge and skills, and the increasing relations of other branches of science and art with mathematics.
The relationship between mathematics and life is quite extensive and generally covers the topics of "mathematical order in nature", "real life problems", "use of mathematics in science and art". The use of mathematics in the sciences covers a large part of the existing mathematical knowledge and the fields in which it is used are also quite extensive. The topics covered in the book are as follows: Golden Ratio (in face, body and dental aesthetics; heart, brain, lungs, gynecology, genetics, walking, finance, marketing, physics, architecture, music and painting), Polyhedrons (applications in different branches of science and art) ), Fibonacci Numbers and their uses, Spirals and Spirals in Nature, Mathematical Order in Plants, Music and Mathematics, Fractals and their Applications in Life (economics, music, genetic music, modeling natural forms, medicine, architecture, urban planning, geology, classification of fingerprints, Classification of trees, graphic design, fractal antenna, photo compression, sculpture and painting) and examples of Mathematical Modeling at the point of solving real life problems. In summary; In this book, the mathematical order of nature and the golden ratio, Fibonacci numbers, fractals and regular polyhedra, which have an important place in nature, life, art, aesthetics and some scientific fields, are emphasized.
Basic knowledge and skills that should be used in daily life such as measuring (number, length, area, volume, time) and calculating (shopping, determining the requirements for the completion of a job, sharing, finding direction, determining relationships, etc.) mark the emergence of mathematics. motivated. Therefore, before mathematical concepts and operations were defined, they were felt in life and the mental infrastructure of discovery was formed. When we consider numbers, shapes and properties, solving real life problems with a mathematical potential, and generally being able to reveal the solution methods to problems, as a mathematical thinking skill; It would be appropriate to define mathematics as an art of thinking. These basic elements have gradually diversified and progressed with the tendency of the mind to develop them, the desire to know and understand, the development of life in a way that will increase the use of mathematical knowledge and skills, and the increasing relations of other branches of science and art with mathematics.
The relationship between mathematics and life is quite extensive and generally covers the topics of "mathematical order in nature", "real life problems", "use of mathematics in science and art". The use of mathematics in the sciences covers a large part of the existing mathematical knowledge and the fields in which it is used are also quite extensive. The topics covered in the book are as follows: Golden Ratio (in face, body and dental aesthetics; heart, brain, lungs, gynecology, genetics, walking, finance, marketing, physics, architecture, music and painting), Polyhedrons (applications in different branches of science and art) ), Fibonacci Numbers and their uses, Spirals and Spirals in Nature, Mathematical Order in Plants, Music and Mathematics, Fractals and their Applications in Life (economics, music, genetic music, modeling natural forms, medicine, architecture, urban planning, geology, classification of fingerprints, Classification of trees, graphic design, fractal antenna, photo compression, sculpture and painting) and examples of Mathematical Modeling at the point of solving real life problems. In summary; In this book, the mathematical order of nature and the golden ratio, Fibonacci numbers, fractals and regular polyhedra, which have an important place in nature, life, art, aesthetics and some scientific fields, are emphasized.
In this book, very important fundamental issues of Differential Equations that can be included in the seminar topics of universities are discussed in order to prepare undergraduate and graduate students. Since DD solutions of Differential Equations can seldom be expressed with implicit formulas, numerical computational methods have been needed over time to approximate their solutions. For this reason, attention has been paid to give the examination properties of DD with the developed numerical solution Finite Element Method (SEM). More than 99% of today's software has been built on the basis of these methods, allowing for high-precision full-scale simulation of engineering structures. In the presented study, the traditional solution methods of Differential Equations are presented in summary form, and their applications are given in parallel with MATLAB tools. Afterwards, the features of using databases in MATLAB are explained and various applications are shown with MATLAB tools, since the analysis of Differential Equations with no implicit solution by SEM requires an extraordinarily large volume of data. For each section, education and training analysis software in MATLAB environment and video presentations of examples are presented in DVD-QR code. This book is of interest to a wide range of professionals, including students, designers, and researchers in the field of Solid Mechanics, Structural Mechanics, adding new color to their education in Differential Equation research.
This book has been prepared for undergraduate, graduate and especially scientific research. In this book, in quantitative, qualitative and mixed research, how the research process (determining the research problem, establishing hypotheses, determining the sampling method, data collection, reliability, validity, analysis of the data, evaluation of the findings, reporting, publication ethics etc.) will be carried out, quantitative, qualitative and mixed research. terms of use of analysis methods, use of package programs (SPSS-AMOS-META) in the analysis of data, statistics specific to the field of health, etc. tried to be given. In quantitative methods, parametric and nonparametric techniques and their differences, analysis methods to be applied according to these differences are given. Similarly, the differences between qualitative methods and the situations to be applied according to these differences are given.
This book, which deals with the basic issues of mathematics teaching at the undergraduate level with the approach of giving lectures in the classroom, is the product of twenty years of experience. In the explanation of the subjects; It has adopted the aim of being able to carry out the mathematical operations that students need, to develop mathematical thinking and to teach mathematical concepts.
In the book; numbers, algebra, functions, derivatives and integrals, which are the basic subjects of mathematical analysis, and vector, matrix, determinant and linear equation systems of linear algebra are explained at a basic level.
The following principles were taken into account in the selection of the exercises in the book:
1. To ensure that the student learns and reinforces the subject,
2. To develop mathematical processing skills and thinking,
3. To convert a given problem statement into a mathematical expression by interpreting the theoretical information.
It is aimed that the Basic and General Mathematics book will be useful to all students.
In the book; numbers, algebra, functions, derivatives and integrals, which are the basic subjects of mathematical analysis, and vector, matrix, determinant and linear equation systems of linear algebra are explained at a basic level.
The following principles were taken into account in the selection of the exercises in the book:
1. To ensure that the student learns and reinforces the subject,
2. To develop mathematical processing skills and thinking,
3. To convert a given problem statement into a mathematical expression by interpreting the theoretical information.
It is aimed that the Basic and General Mathematics book will be useful to all students.
The book presented by the author to the members of the jury as a “Professor Presentation” is the first of the 6-book Statistics Series. "Regression and Correlation Analysis", which is one of the most fundamental subjects of "statistics", which in a sense forms the basis of "Multivariate Statistical Methods", is discussed in detail in the book, which was published for the first time in 1996, for the second edition in 2002 and for the third edition in 2017.
As it is known, this analysis, which is one of the most frequently used methods in determining "Forecast and Policy" especially in Business Administration, is examined theoretically by distinguishing between population and sample in the book, the validity of the assumptions is examined, and how to find solutions for deviations from the assumptions, if any, is included. Applications are presented both with detailed solutions and as computer (SPSS Program) outputs.
As it is known, this analysis, which is one of the most frequently used methods in determining "Forecast and Policy" especially in Business Administration, is examined theoretically by distinguishing between population and sample in the book, the validity of the assumptions is examined, and how to find solutions for deviations from the assumptions, if any, is included. Applications are presented both with detailed solutions and as computer (SPSS Program) outputs.