This document outlines the course requirements for a pre-PhD program in mathematics. It includes 1) a required 5-credit research methodology course covering skills like LaTeX, mathematical software, and reviewing papers; 2) an optional 5-credit participation in an advanced training mathematics school; and 3) a variety of 5-credit optional courses in areas like differential equations, Fourier analysis, complex analysis, and more. Students must complete 20 total credits, including the required methodology course, 10 credits from two other optional courses, and an additional 5-credit reading course with their research guide.
1. Determinants are defined using arrangements of numbers. An arrangement is an ordered list where the numbers can be in any order.
2. Any rearrangement of the numbers in a fixed arrangement will go through all possible arrangements. Similarly, if one variable ranges over all arrangements, then the numbers assigned based on its ordering will also go through all arrangements.
3. These properties of arrangements are used to define determinants and prove their basic properties. Determinants provide a way to compute a quantity that transforms in a predictable way under rearrangements of the numbers.
ON THE CATEGORY OF ORDERED TOPOLOGICAL MODULES OPTIMIZATION AND LAGRANGE’S PR...IJESM JOURNAL
A category is an algebraic structure made up of a collection of objects linked together by morphisms. As a foundation of mathematics, categories were created as a way of relating algebraic structures and systems of topological spaces In this paper we define a derivative using cones in the category of topological modules and use the Lagrange’s principle to obtain optimization results in the category.
A typical mathematics system has four parts: undefined terms which cannot be precisely defined but are chosen arbitrarily to facilitate development; defined terms which are defined in terms of undefined terms; axioms and postulates which are general truths that form the basis of the system; and theorems which are statements derived from successive application of axioms and previously proved statements.
This chapter discusses motion in two dimensions, including vectors, projectile motion, and uniform circular motion. Key concepts are distinguishing scalars from vectors, adding and subtracting vectors analytically and graphically, and describing position, velocity, and acceleration as vectors. Projectile motion equations give the horizontal and vertical motion of a projectile. Uniform circular motion describes constant speed but changing direction, with equations for centripetal acceleration. Example problems apply these concepts.
The document discusses the discrete mathematics curriculum at Saint-Petersburg Electrotechnical University. It provides an overview of which discrete math topics are covered in each year of study for different degree programs. It also compares course parameters like credits and hours between the university and TUT. Key modules covered in the second year Math Logic and Algorithm Theory course are outlined. Competencies addressed in the curriculum are mapped to SEFI levels, with additional competencies covered uniquely at the university. Suggested modifications to improve the curriculum structure are presented.
Bland, Paul E.
Rings and their modules / by Paul E. Bland.
p. cm.(De Gruyter textbook)
Includes bibliographical references and index.
ISBN 978-3-11-025022-0 (alk. paper)
1. Rings (Algebra) 2. Modules (Algebra) I. Title.
QA247.B545 2011
5121.4dc22
2010034731
This document provides information about an algebra course offered at the university. The course aims to develop students' algebraic knowledge and skills so they can apply algebra in bioscience calculations. It covers fundamental algebra concepts, equations, inequalities, functions and graphs, sequences and series, matrices, vectors, and mathematical modeling. The course is offered in semester 1 and involves 28 lectures, 14 tutorials, and 78 hours of independent study over the semester for a total of 120 hours. Student learning outcomes include describing polynomial functions, illustrating various function types, and selecting mathematical models. The course is assessed through exams, tests, quizzes, assignments, and projects.
1. Determinants are defined using arrangements of numbers. An arrangement is an ordered list where the numbers can be in any order.
2. Any rearrangement of the numbers in a fixed arrangement will go through all possible arrangements. Similarly, if one variable ranges over all arrangements, then the numbers assigned based on its ordering will also go through all arrangements.
3. These properties of arrangements are used to define determinants and prove their basic properties. Determinants provide a way to compute a quantity that transforms in a predictable way under rearrangements of the numbers.
ON THE CATEGORY OF ORDERED TOPOLOGICAL MODULES OPTIMIZATION AND LAGRANGE’S PR...IJESM JOURNAL
A category is an algebraic structure made up of a collection of objects linked together by morphisms. As a foundation of mathematics, categories were created as a way of relating algebraic structures and systems of topological spaces In this paper we define a derivative using cones in the category of topological modules and use the Lagrange’s principle to obtain optimization results in the category.
A typical mathematics system has four parts: undefined terms which cannot be precisely defined but are chosen arbitrarily to facilitate development; defined terms which are defined in terms of undefined terms; axioms and postulates which are general truths that form the basis of the system; and theorems which are statements derived from successive application of axioms and previously proved statements.
This chapter discusses motion in two dimensions, including vectors, projectile motion, and uniform circular motion. Key concepts are distinguishing scalars from vectors, adding and subtracting vectors analytically and graphically, and describing position, velocity, and acceleration as vectors. Projectile motion equations give the horizontal and vertical motion of a projectile. Uniform circular motion describes constant speed but changing direction, with equations for centripetal acceleration. Example problems apply these concepts.
The document discusses the discrete mathematics curriculum at Saint-Petersburg Electrotechnical University. It provides an overview of which discrete math topics are covered in each year of study for different degree programs. It also compares course parameters like credits and hours between the university and TUT. Key modules covered in the second year Math Logic and Algorithm Theory course are outlined. Competencies addressed in the curriculum are mapped to SEFI levels, with additional competencies covered uniquely at the university. Suggested modifications to improve the curriculum structure are presented.
Bland, Paul E.
Rings and their modules / by Paul E. Bland.
p. cm.(De Gruyter textbook)
Includes bibliographical references and index.
ISBN 978-3-11-025022-0 (alk. paper)
1. Rings (Algebra) 2. Modules (Algebra) I. Title.
QA247.B545 2011
5121.4dc22
2010034731
This document provides information about an algebra course offered at the university. The course aims to develop students' algebraic knowledge and skills so they can apply algebra in bioscience calculations. It covers fundamental algebra concepts, equations, inequalities, functions and graphs, sequences and series, matrices, vectors, and mathematical modeling. The course is offered in semester 1 and involves 28 lectures, 14 tutorials, and 78 hours of independent study over the semester for a total of 120 hours. Student learning outcomes include describing polynomial functions, illustrating various function types, and selecting mathematical models. The course is assessed through exams, tests, quizzes, assignments, and projects.
The document provides an introduction to calculus concepts including:
- Sets can represent collections of objects and are denoted using curly brackets. There are five regular solids that follow the Euler formula relating the number of faces, vertices and edges of each solid.
- The preface outlines the main purposes and organization of the two-volume calculus text, which includes fundamental concepts, applications, proofs, and multiple approaches.
- Volume I contains 5 chapters covering sets, functions, graphs, limits, differential calculus, integral calculus, sequences, summations, and applications of calculus.
This document outlines the proposed syllabus for a Master of Science in Mathematics program to be implemented in the 2020-21 academic year. It includes 10 core courses to be taken over two semesters. The courses cover topics in group theory, ring theory, real analysis, topology, linear algebra, field theory, measure theory, advanced topology, classical mechanics, and students can choose one core elective course from options like numerical analysis, differential equations, calculus of variations, number theory, fuzzy mathematics, and others. For each course, the document lists the course code, credit hours, and a brief description of the topics to be covered in 4 units. Required textbooks and reference materials are also provided for each course.
This document outlines the course objectives and modules for a mathematical foundations of computing course. The course objectives are to formulate physical phenomena using matrices, apply differentiation and integration techniques, and analyze periodic signals using Fourier series. The 6 modules cover topics including linear algebra with matrices, matrix eigenproblems, differential calculus, integral calculus, multiple integration, and Fourier series. The course aims to apply these mathematical concepts to real-world domains such as traffic networks, geography, finance, fluid dynamics, remote sensing, audio/video compression, and more. Recommended textbooks and references are also provided.
This document provides information about a course on transform calculus, Fourier series, and numerical techniques. It includes 5 modules that will cover topics like Laplace transforms, Fourier series, Fourier transforms, difference equations, numerical solutions to ODEs, and calculus of variations. It lists learning objectives, topics to be covered in each module, textbook references, course outcomes, and the question paper pattern. The course aims to provide an understanding of various advanced mathematical concepts and their applications in engineering.
Advanced Linear Algebra (Third Edition) By Steven RomanLisa Cain
This document provides information about the Graduate Texts in Mathematics series published by Springer Science+Business Media, LLC. It lists 75 books in the series along with their authors and topics. It also provides the names of the editorial board members for the series, Steven Axler and Kenneth Ribet.
This document outlines the proposed syllabus for the third and fourth semesters of the M.Sc. Mathematics program under the Choice Based Credit System. The third semester includes core courses in Complex Analysis, Functional Analysis, Mathematical Methods, and a core elective course that can be selected from options like Fluid Dynamics, General Relativity, and Graph Theory. It also includes a foundation course that can be selected from options in different fields. Similarly, the fourth semester outlines core courses in Dynamical Systems, Partial Differential Equations, Integral Equations, and a core elective course that can be selected from options like Fluid Dynamics, Cosmology and Combinatorics, along with a foundation course. Detailed course contents are provided
A Course In LINEAR ALGEBRA With ApplicationsNathan Mathis
This document provides the preface and table of contents for the textbook "A Course in Linear Algebra with Applications" by Derek J. S. Robinson. The preface to the second edition notes the addition of a new chapter on linear programming. The preface to the first edition outlines the scope and intended audience of the textbook, which aims to provide a comprehensive introduction to linear algebra while also presenting selected applications. The table of contents provides an overview of the 9 chapters that make up the textbook, covering topics such as matrix algebra, systems of linear equations, determinants, vector spaces, linear transformations, eigenvectors and eigenvalues.
(Graduate Texts in Mathematics) Jurgen Herzog, Takayuki Hibi, Hidefumi Ohsugi...Bui Loi
This document provides an overview of the book "Binomial Ideals" by Herzog, Hibi, and Ohsugi. It discusses the following key points in 3 sentences:
1) The book provides a comprehensive analysis of the algebraic properties of binomial ideals, including their primary decompositions. 2) It covers various topics related to binomial ideals from viewpoints of both commutative algebra and combinatorics, with a focus on applications to statistics. 3) Each chapter discusses a different aspect of binomial ideals, such as edge rings and edge polytopes of graphs, join-meet ideals of lattices, and binomial ideals arising in statistics.
This document discusses the application of finite element exterior calculus to evolution problems. It introduces the concept of Hilbert complexes, which allow the abstraction of essential properties of function spaces and their approximations. Differential forms and operators like the exterior derivative are used to elegantly formulate elliptic problems like the heat, wave, Poisson, and Maxwell equations. Approximation theory for subcomplexes and non-subcomplexes is developed. Finally, methods are discussed for the semidiscretization and discretization of parabolic problems like the heat equation using these concepts.
This document provides an introduction and outline for a textbook on abstract and linear algebra. The textbook aims to teach these topics as a coherent discipline rather than separate courses. It is intended for undergraduate mathematics, computer science, and physical science students. The introduction describes the motivation and background for how the textbook was developed, structured in a linear fashion to build upon previous topics. It also outlines the chapters, which cover topics like groups, rings, matrices, modules, and linear algebra.
This document outlines the syllabus for a course on analysis of algorithms and complexity. The course will cover foundational topics like asymptotic analysis and randomized algorithms, as well as specific algorithms like sorting, searching trees, and graph algorithms. It will also cover advanced techniques like dynamic programming, greedy algorithms, and amortized analysis. Later topics will include NP-completeness, multi-threaded algorithms, and approaches for dealing with NP-complete problems. The requirements include exams, homework assignments, and a project, and the course will be taught in English.
This document provides an overview of a graduate-level textbook on stochastic calculus. The textbook covers key topics like Brownian motion, martingales, stochastic integration and stochastic differential equations. It is intended to provide students with a rigorous yet concise introduction to the theory and techniques of stochastic calculus for continuous semimartingales. The textbook includes 9 chapters that build upon each other and numerous exercises are provided to help readers master the calculus techniques.
This document provides an overview of the book "Multiplicative Number Theory I: Classical Theory" by Hugh L. Montgomery and Robert C. Vaughan. The book comprehensively covers the fundamental topics in multiplicative number theory and the distribution of prime numbers, assuming only an undergraduate degree in mathematics. It is based on courses taught by the authors and is intended to prepare students for research-level work in analytic number theory. The book includes over 500 exercises and draws on the authors' extensive research experience.
The document outlines the syllabus for mathematics in classes 9 and 10. It includes 6 units for class 9 (Number Systems, Algebra, Coordinate Geometry, Geometry, Mensuration, Statistics and Probability) and 7 units for class 10 (Number Systems, Algebra, Coordinate Geometry, Geometry, Trigonometry, Mensuration, Statistics and Probability). The objectives of teaching mathematics are to consolidate skills, develop logical thinking, apply knowledge to solve problems, and develop interest in the subject. Assessment includes pen and paper tests, portfolios, and practical lab activities.
CBSE Math 9 & 10 Syllabus - LearnConnectEdLearnConnectEd
The document outlines the syllabus for mathematics in classes 9 and 10. It includes 6 units for class 9 (Number Systems, Algebra, Coordinate Geometry, Geometry, Mensuration, Statistics & Probability) and 7 units for class 10 (Number Systems, Algebra, Coordinate Geometry, Geometry, Trigonometry, Mensuration, Statistics & Probability). The objectives are to consolidate mathematical knowledge and skills, develop logical thinking and the ability to apply concepts to solve problems. Assessment includes pen and paper tests, portfolios and practical lab activities.
The document outlines the syllabus for Applied Mathematics - 1 for the first semester of the FY D(IT) program at the Maharaja Sayajirao University of Baroda. The syllabus covers 6 units: 1) reorientation of surds, logarithms, binomial theorem, and progressions, 2) limits and continuity, 3) differentiation, 4) equations of straight lines, circles, ellipses, hyperbolas, and parabolas, 5) reorientation of trigonometric functions, and 6) properties of triangles including sine, cosine, and projection formulas. Students will learn concepts and solve problems related to these mathematical topics over the course of the semester.
This document provides proposed syllabi for courses in the BSc Mathematics program at Mahatma Gandhi Arts, Science and Commerce College for semesters 5 and 6. It includes proposed courses, topics to be covered, reference materials, and exam details for Skill Enhancement Courses, Discipline Specific Electives, and other mathematics courses. Courses cover topics such as probability, mathematical modeling, linear algebra, matrices, numerical methods, graph theory, Boolean algebra, complex analysis, vector calculus, linear programming, and transportation problems. Exams will be conducted by the college for SEC courses and the university for DSE courses.
This document provides the title page and preface for the third edition of the textbook "Abstract Algebra" by I.N. Herstein. The title page lists the author, title, edition number, and publisher. The preface explains that the third edition aims to preserve Herstein's style while correcting errors and expanding some proofs. It also suggests an alternative approach for instructors who want to introduce permutations earlier. The preface thanks reviewers for their helpful comments.
The document outlines the syllabus for the Engineering Mathematics - I course, covering topics in differential and integral calculus, vector calculus, differential equations, and linear algebra. It includes 8 units of study with topics such as derivatives, indeterminate forms, partial differentiation, and vector identities. The syllabus also provides details on textbook and reference materials for the course.
This document provides a summary of 18 new books available at the library. The books cover a wide range of topics including quality engineering, Zariski geometries, singularity theory, probability, graph theory, isoperimetric problems, number theory, non-Hermitian quantum mechanics, multiphysics modeling, quantum computation, biofuels, irrigation management, biomass combustion, concrete design, steel bridge design, signal analysis, and elliptic curves. Publication years of the books range from 2001 to 2011. Each entry provides the book title, author, a brief description, and call number.
This presentation includes basic of PCOS their pathology and treatment and also Ayurveda correlation of PCOS and Ayurvedic line of treatment mentioned in classics.
The document provides an introduction to calculus concepts including:
- Sets can represent collections of objects and are denoted using curly brackets. There are five regular solids that follow the Euler formula relating the number of faces, vertices and edges of each solid.
- The preface outlines the main purposes and organization of the two-volume calculus text, which includes fundamental concepts, applications, proofs, and multiple approaches.
- Volume I contains 5 chapters covering sets, functions, graphs, limits, differential calculus, integral calculus, sequences, summations, and applications of calculus.
This document outlines the proposed syllabus for a Master of Science in Mathematics program to be implemented in the 2020-21 academic year. It includes 10 core courses to be taken over two semesters. The courses cover topics in group theory, ring theory, real analysis, topology, linear algebra, field theory, measure theory, advanced topology, classical mechanics, and students can choose one core elective course from options like numerical analysis, differential equations, calculus of variations, number theory, fuzzy mathematics, and others. For each course, the document lists the course code, credit hours, and a brief description of the topics to be covered in 4 units. Required textbooks and reference materials are also provided for each course.
This document outlines the course objectives and modules for a mathematical foundations of computing course. The course objectives are to formulate physical phenomena using matrices, apply differentiation and integration techniques, and analyze periodic signals using Fourier series. The 6 modules cover topics including linear algebra with matrices, matrix eigenproblems, differential calculus, integral calculus, multiple integration, and Fourier series. The course aims to apply these mathematical concepts to real-world domains such as traffic networks, geography, finance, fluid dynamics, remote sensing, audio/video compression, and more. Recommended textbooks and references are also provided.
This document provides information about a course on transform calculus, Fourier series, and numerical techniques. It includes 5 modules that will cover topics like Laplace transforms, Fourier series, Fourier transforms, difference equations, numerical solutions to ODEs, and calculus of variations. It lists learning objectives, topics to be covered in each module, textbook references, course outcomes, and the question paper pattern. The course aims to provide an understanding of various advanced mathematical concepts and their applications in engineering.
Advanced Linear Algebra (Third Edition) By Steven RomanLisa Cain
This document provides information about the Graduate Texts in Mathematics series published by Springer Science+Business Media, LLC. It lists 75 books in the series along with their authors and topics. It also provides the names of the editorial board members for the series, Steven Axler and Kenneth Ribet.
This document outlines the proposed syllabus for the third and fourth semesters of the M.Sc. Mathematics program under the Choice Based Credit System. The third semester includes core courses in Complex Analysis, Functional Analysis, Mathematical Methods, and a core elective course that can be selected from options like Fluid Dynamics, General Relativity, and Graph Theory. It also includes a foundation course that can be selected from options in different fields. Similarly, the fourth semester outlines core courses in Dynamical Systems, Partial Differential Equations, Integral Equations, and a core elective course that can be selected from options like Fluid Dynamics, Cosmology and Combinatorics, along with a foundation course. Detailed course contents are provided
A Course In LINEAR ALGEBRA With ApplicationsNathan Mathis
This document provides the preface and table of contents for the textbook "A Course in Linear Algebra with Applications" by Derek J. S. Robinson. The preface to the second edition notes the addition of a new chapter on linear programming. The preface to the first edition outlines the scope and intended audience of the textbook, which aims to provide a comprehensive introduction to linear algebra while also presenting selected applications. The table of contents provides an overview of the 9 chapters that make up the textbook, covering topics such as matrix algebra, systems of linear equations, determinants, vector spaces, linear transformations, eigenvectors and eigenvalues.
(Graduate Texts in Mathematics) Jurgen Herzog, Takayuki Hibi, Hidefumi Ohsugi...Bui Loi
This document provides an overview of the book "Binomial Ideals" by Herzog, Hibi, and Ohsugi. It discusses the following key points in 3 sentences:
1) The book provides a comprehensive analysis of the algebraic properties of binomial ideals, including their primary decompositions. 2) It covers various topics related to binomial ideals from viewpoints of both commutative algebra and combinatorics, with a focus on applications to statistics. 3) Each chapter discusses a different aspect of binomial ideals, such as edge rings and edge polytopes of graphs, join-meet ideals of lattices, and binomial ideals arising in statistics.
This document discusses the application of finite element exterior calculus to evolution problems. It introduces the concept of Hilbert complexes, which allow the abstraction of essential properties of function spaces and their approximations. Differential forms and operators like the exterior derivative are used to elegantly formulate elliptic problems like the heat, wave, Poisson, and Maxwell equations. Approximation theory for subcomplexes and non-subcomplexes is developed. Finally, methods are discussed for the semidiscretization and discretization of parabolic problems like the heat equation using these concepts.
This document provides an introduction and outline for a textbook on abstract and linear algebra. The textbook aims to teach these topics as a coherent discipline rather than separate courses. It is intended for undergraduate mathematics, computer science, and physical science students. The introduction describes the motivation and background for how the textbook was developed, structured in a linear fashion to build upon previous topics. It also outlines the chapters, which cover topics like groups, rings, matrices, modules, and linear algebra.
This document outlines the syllabus for a course on analysis of algorithms and complexity. The course will cover foundational topics like asymptotic analysis and randomized algorithms, as well as specific algorithms like sorting, searching trees, and graph algorithms. It will also cover advanced techniques like dynamic programming, greedy algorithms, and amortized analysis. Later topics will include NP-completeness, multi-threaded algorithms, and approaches for dealing with NP-complete problems. The requirements include exams, homework assignments, and a project, and the course will be taught in English.
This document provides an overview of a graduate-level textbook on stochastic calculus. The textbook covers key topics like Brownian motion, martingales, stochastic integration and stochastic differential equations. It is intended to provide students with a rigorous yet concise introduction to the theory and techniques of stochastic calculus for continuous semimartingales. The textbook includes 9 chapters that build upon each other and numerous exercises are provided to help readers master the calculus techniques.
This document provides an overview of the book "Multiplicative Number Theory I: Classical Theory" by Hugh L. Montgomery and Robert C. Vaughan. The book comprehensively covers the fundamental topics in multiplicative number theory and the distribution of prime numbers, assuming only an undergraduate degree in mathematics. It is based on courses taught by the authors and is intended to prepare students for research-level work in analytic number theory. The book includes over 500 exercises and draws on the authors' extensive research experience.
The document outlines the syllabus for mathematics in classes 9 and 10. It includes 6 units for class 9 (Number Systems, Algebra, Coordinate Geometry, Geometry, Mensuration, Statistics and Probability) and 7 units for class 10 (Number Systems, Algebra, Coordinate Geometry, Geometry, Trigonometry, Mensuration, Statistics and Probability). The objectives of teaching mathematics are to consolidate skills, develop logical thinking, apply knowledge to solve problems, and develop interest in the subject. Assessment includes pen and paper tests, portfolios, and practical lab activities.
CBSE Math 9 & 10 Syllabus - LearnConnectEdLearnConnectEd
The document outlines the syllabus for mathematics in classes 9 and 10. It includes 6 units for class 9 (Number Systems, Algebra, Coordinate Geometry, Geometry, Mensuration, Statistics & Probability) and 7 units for class 10 (Number Systems, Algebra, Coordinate Geometry, Geometry, Trigonometry, Mensuration, Statistics & Probability). The objectives are to consolidate mathematical knowledge and skills, develop logical thinking and the ability to apply concepts to solve problems. Assessment includes pen and paper tests, portfolios and practical lab activities.
The document outlines the syllabus for Applied Mathematics - 1 for the first semester of the FY D(IT) program at the Maharaja Sayajirao University of Baroda. The syllabus covers 6 units: 1) reorientation of surds, logarithms, binomial theorem, and progressions, 2) limits and continuity, 3) differentiation, 4) equations of straight lines, circles, ellipses, hyperbolas, and parabolas, 5) reorientation of trigonometric functions, and 6) properties of triangles including sine, cosine, and projection formulas. Students will learn concepts and solve problems related to these mathematical topics over the course of the semester.
This document provides proposed syllabi for courses in the BSc Mathematics program at Mahatma Gandhi Arts, Science and Commerce College for semesters 5 and 6. It includes proposed courses, topics to be covered, reference materials, and exam details for Skill Enhancement Courses, Discipline Specific Electives, and other mathematics courses. Courses cover topics such as probability, mathematical modeling, linear algebra, matrices, numerical methods, graph theory, Boolean algebra, complex analysis, vector calculus, linear programming, and transportation problems. Exams will be conducted by the college for SEC courses and the university for DSE courses.
This document provides the title page and preface for the third edition of the textbook "Abstract Algebra" by I.N. Herstein. The title page lists the author, title, edition number, and publisher. The preface explains that the third edition aims to preserve Herstein's style while correcting errors and expanding some proofs. It also suggests an alternative approach for instructors who want to introduce permutations earlier. The preface thanks reviewers for their helpful comments.
The document outlines the syllabus for the Engineering Mathematics - I course, covering topics in differential and integral calculus, vector calculus, differential equations, and linear algebra. It includes 8 units of study with topics such as derivatives, indeterminate forms, partial differentiation, and vector identities. The syllabus also provides details on textbook and reference materials for the course.
This document provides a summary of 18 new books available at the library. The books cover a wide range of topics including quality engineering, Zariski geometries, singularity theory, probability, graph theory, isoperimetric problems, number theory, non-Hermitian quantum mechanics, multiphysics modeling, quantum computation, biofuels, irrigation management, biomass combustion, concrete design, steel bridge design, signal analysis, and elliptic curves. Publication years of the books range from 2001 to 2011. Each entry provides the book title, author, a brief description, and call number.
This presentation includes basic of PCOS their pathology and treatment and also Ayurveda correlation of PCOS and Ayurvedic line of treatment mentioned in classics.
How to Make a Field Mandatory in Odoo 17Celine George
In Odoo, making a field required can be done through both Python code and XML views. When you set the required attribute to True in Python code, it makes the field required across all views where it's used. Conversely, when you set the required attribute in XML views, it makes the field required only in the context of that particular view.
Reimagining Your Library Space: How to Increase the Vibes in Your Library No ...Diana Rendina
Librarians are leading the way in creating future-ready citizens – now we need to update our spaces to match. In this session, attendees will get inspiration for transforming their library spaces. You’ll learn how to survey students and patrons, create a focus group, and use design thinking to brainstorm ideas for your space. We’ll discuss budget friendly ways to change your space as well as how to find funding. No matter where you’re at, you’ll find ideas for reimagining your space in this session.
LAND USE LAND COVER AND NDVI OF MIRZAPUR DISTRICT, UPRAHUL
This Dissertation explores the particular circumstances of Mirzapur, a region located in the
core of India. Mirzapur, with its varied terrains and abundant biodiversity, offers an optimal
environment for investigating the changes in vegetation cover dynamics. Our study utilizes
advanced technologies such as GIS (Geographic Information Systems) and Remote sensing to
analyze the transformations that have taken place over the course of a decade.
The complex relationship between human activities and the environment has been the focus
of extensive research and worry. As the global community grapples with swift urbanization,
population expansion, and economic progress, the effects on natural ecosystems are becoming
more evident. A crucial element of this impact is the alteration of vegetation cover, which plays a
significant role in maintaining the ecological equilibrium of our planet.Land serves as the foundation for all human activities and provides the necessary materials for
these activities. As the most crucial natural resource, its utilization by humans results in different
'Land uses,' which are determined by both human activities and the physical characteristics of the
land.
The utilization of land is impacted by human needs and environmental factors. In countries
like India, rapid population growth and the emphasis on extensive resource exploitation can lead
to significant land degradation, adversely affecting the region's land cover.
Therefore, human intervention has significantly influenced land use patterns over many
centuries, evolving its structure over time and space. In the present era, these changes have
accelerated due to factors such as agriculture and urbanization. Information regarding land use and
cover is essential for various planning and management tasks related to the Earth's surface,
providing crucial environmental data for scientific, resource management, policy purposes, and
diverse human activities.
Accurate understanding of land use and cover is imperative for the development planning
of any area. Consequently, a wide range of professionals, including earth system scientists, land
and water managers, and urban planners, are interested in obtaining data on land use and cover
changes, conversion trends, and other related patterns. The spatial dimensions of land use and
cover support policymakers and scientists in making well-informed decisions, as alterations in
these patterns indicate shifts in economic and social conditions. Monitoring such changes with the
help of Advanced technologies like Remote Sensing and Geographic Information Systems is
crucial for coordinated efforts across different administrative levels. Advanced technologies like
Remote Sensing and Geographic Information Systems
9
Changes in vegetation cover refer to variations in the distribution, composition, and overall
structure of plant communities across different temporal and spatial scales. These changes can
occur natural.
A review of the growth of the Israel Genealogy Research Association Database Collection for the last 12 months. Our collection is now passed the 3 million mark and still growing. See which archives have contributed the most. See the different types of records we have, and which years have had records added. You can also see what we have for the future.
How to Manage Your Lost Opportunities in Odoo 17 CRMCeline George
Odoo 17 CRM allows us to track why we lose sales opportunities with "Lost Reasons." This helps analyze our sales process and identify areas for improvement. Here's how to configure lost reasons in Odoo 17 CRM
This slide is special for master students (MIBS & MIFB) in UUM. Also useful for readers who are interested in the topic of contemporary Islamic banking.
Beyond Degrees - Empowering the Workforce in the Context of Skills-First.pptxEduSkills OECD
Iván Bornacelly, Policy Analyst at the OECD Centre for Skills, OECD, presents at the webinar 'Tackling job market gaps with a skills-first approach' on 12 June 2024
Leveraging Generative AI to Drive Nonprofit InnovationTechSoup
In this webinar, participants learned how to utilize Generative AI to streamline operations and elevate member engagement. Amazon Web Service experts provided a customer specific use cases and dived into low/no-code tools that are quick and easy to deploy through Amazon Web Service (AWS.)
বাংলাদেশের অর্থনৈতিক সমীক্ষা ২০২৪ [Bangladesh Economic Review 2024 Bangla.pdf] কম্পিউটার , ট্যাব ও স্মার্ট ফোন ভার্সন সহ সম্পূর্ণ বাংলা ই-বুক বা pdf বই " সুচিপত্র ...বুকমার্ক মেনু 🔖 ও হাইপার লিংক মেনু 📝👆 যুক্ত ..
আমাদের সবার জন্য খুব খুব গুরুত্বপূর্ণ একটি বই ..বিসিএস, ব্যাংক, ইউনিভার্সিটি ভর্তি ও যে কোন প্রতিযোগিতা মূলক পরীক্ষার জন্য এর খুব ইম্পরট্যান্ট একটি বিষয় ...তাছাড়া বাংলাদেশের সাম্প্রতিক যে কোন ডাটা বা তথ্য এই বইতে পাবেন ...
তাই একজন নাগরিক হিসাবে এই তথ্য গুলো আপনার জানা প্রয়োজন ...।
বিসিএস ও ব্যাংক এর লিখিত পরীক্ষা ...+এছাড়া মাধ্যমিক ও উচ্চমাধ্যমিকের স্টুডেন্টদের জন্য অনেক কাজে আসবে ...
বাংলাদেশ অর্থনৈতিক সমীক্ষা (Economic Review) ২০২৪ UJS App.pdf
8 methematics
1. Pre-Ph.D. Course Mathematics
1) Research Methodology (Mathematics) (5 credits) (Compulsory)
1. LaTeX and Beamer (10 hours)
2. At least one Mathematical software out of the following: Scilab /KASH/ Maxima/ SAGE/
Other software suggested by the research guide (10hours)
3. Working knowledge of MathSciNet, JSTORE and other online journals, Review of a
research paper (4 hours)
4. Rapid Reader: Mathematics and its History, by J. Stillwell, Springer International
Edition, 4th Indian Reprint, 2005. (10 hours)
5. Participating in seminar/lecture son different topics in Mathematics (6 hoarse)
2) ATM School Participation (5 credits) (Optional )
Advanced Training in Mathematics (ATM) school have been devised by National
Board for Higher Mathematics to broaden the knowledge of a research student in
Mathematics and also inculcating problem solving skills for better understanding of the
subject and developing research orientation. A student participating in an NBHM sponsored
ATM school of 3-4 weeks duration such as Annual Foundation School I for II or an
Advanced Instructional School on a specific topic will earn 5 credits provided the school is
attended after getting provisional admission for Ph.D. The Research Guide will request the
coordinator of the school to give a grade to the student based on the participation of the
student in the ATM school.
3) Differential Equations (5 credits) (Optional )
(A) Revision:
1. Linear system of ordinary differential equation, symptotic stability, existence
uniqueness theorems.
2. Elementary Practical Differential Equations. Laplace, Heat and wave equations.
Separation of variable method.
(B) Classification and Characteristics of Higher Order PDFs: Cauchy-Kovalevskaya
Theorem. Holmgren’s Uniqueness Theorem.
(C) Conservation Laws and Shocks systems in one dimension : conservation laws, weak
solution, Lax Shock Solution, Riemann Problems, Dirichlet Problem. Maximum
Principles for parabolic equations; (i) weak maximum principle, (ii) strong maximum
principle.
Reference Books:
1. An Introduction to Partial Differential Equations, M. Renardy & R. C.
Rogers (Springer), (Second Edition).
2. Differential Equations, Dynamical Systems and an Introduction to Chaos, 2nd Edn., by
MW. Hirsch, S. Smale, R. L. Devaney, Elsevier, 2004
2. 4) Fourier Series and Functional Analysis (5 Credits) (Optional)
Conditional, unconditional and absolute convergence of a series in a normed linear space;
notion of an orthonormal basis for a Hilbert space Trigonometric series, Fourier series,
Fourier sine and consine series Piecewise continuous/smooth functions, absolutely
continuous functions, functions of bounded variation (and their significance in the theory of
Fourier series) Generalized Riemann-Lebesgue lemma Dirichlet and Fourier kernels
Convergence of Fourier series Discussion (Without proofs) of some of the following topics:
The Gibbs phenomenon, divergent Fourier series, term-by-term operations on Fourier series,
various kinks of summability, Fejer theory, multivariable Fourier series.
Reference:
1. Georage Bachman, Lawrence Narici and Edward Beakenstein, Fourier and Wavelet
Analysis, Springer-Verlag, New York, 2000
2. Richard L. Wheeden and Antoni Zygmund, Measure and integral, Marcel Dekker Inc.,
New York, 1977.
3. Balmohan V. Limaye, Functional Analysis, New Age International (P) Ltd. New Delhi,
2004.
5) Complex Analysis (5 Credits) (Optional)
(1) Analytic functions, Path integrals, Winding number, Cauchy integral formula and
consequences. Gap theorem, Isolated singularities, Residue theorem, Liouville theorem.
(2) Casorati- Weierstrass therorem, Bloch-Landau therorem, Picard’s therorems, Mobius
transformations, Schwartz lemma, External metrics, Riemann mapping theorem,
Argument principle, Rouche’s therorem..
(3) Runge’s theorem, Infinite products, Weierstrass p-function, Mittag-Leffler expansion.
References:
1. Murali Rap & H. Stetkaer, Complex Analysis, World Scinetific, 1991.
2. L. V. Ahlfors, Complex Analysis, McGraw-Hill, Inc., 1996.
3. A. R. Shastri, Complex Analysis, 2010.
4. S. G. Krantz, Complex Analysis: The Geometric View Points, Second edition, Carus
Math. Monographs, MAA.
6) Commutative Algebra (5 Credits) (Optional)
Prime ideals and maximal ideals, Zariski topology, Nil and Jacobson, radicals, Localization
of rings and modules, Noetherian rings, Hilbert Basis theorem, modules, primary
decomposition, integral dependence, Noether normalization lemma, Krull’s principal ideal
3. theorem, Hilbert’s Null-stellensatz, Structure of artinian rings, Dedekind domains.
Introduction to Algebraic Number Theory. Discriminants of number field.
Factroisation of ideals. Finiteness of class number. Euclidean number rings.
Text-book:
1. Paul Ribenboim, Algebraic Number Theory.
Additional References:
2. M. F. Atiyah and I. G. Macdonald, Introduction to commutative algebra.
3. P. Samuel, Algebraic Number Theory.
1) Algebraic Graph Theory (5 Credits) (Optional)
0. Introduction: Graph theory, Linear algebra. Group theory.
1. Eigenvalues of graphs: Some examples. Eignvalus and walks, Eigenvalues and labllings
of graphs, Lower bounds for the eigenvalues, Upper bounds for the Eigenvalues, Other
matrices related to graphs, Cospectral graphs.
2. Spectral graph theory, Star sets and star partitions, Star completes, Exceptional graphs,
Reconstructing the characteristic polynomial, Non-complete extended p-sums of graphs,
Integral graphs
3. Graph Laplacians. The Laplacian of a graph, Laplace eigenvalues, Eigenvalues and
vertex partitions of graph, The max-cut problem and semi-definite programming,
Isoperimetric inequalities, The traveling salesman problem, Random walks on graphs.
4. Auromorphisms of graphs: Graph auromorphisms, Algorithmic aspects, Automorphisms
of typical graphs, permutation groups, Abstract groups, Cayley graphs, Vertex-transitive
graphs.
5. Distance-transitive graphs: Distance-transitivity, Graphs from groups, Combinatorial
properties, imprimitivity, Bounds, Finite simple groups, The first step, The affine case,
The simple scole case.
6. Computing with graphs and groups: Permutation group algorithms, Strong and accessing
a G-graph, Constructing G-graphs, graph, G-breadth-first search in a G-graph,
Automorphism groups and graph is isomorphism, Computing with vertex-transitive
graphs, Coset enumeration, Coset enumeration for symmetric graphs.
Book : Topics in Algebraic Graph Theory.
Authors : L. W. Beinke and R. J. Wilson
Publisher : Cambridge University Press
8) Course suggested by the Research Guide (5 Credits) (Optional)
There will be a course conducted by the research guide of the Ph.D. student. As per the
recommendation of the guide, the student may take a reading course
With the guide or one of the optional courses in liu of it.
4. 9) If found necessary, course work may be carried out by doctoral
Candidates in sister Departments/Institutes either within or outside the University for
Which
due credit will be given to them. The student.
Can opt for such a course upon recommendation of the Guide and the Chairman,
Ph.D. committee/HOD. Such course-work done outside the department should be restricted
to 10 credit points.
The total number of credits the student should get in the pre-Ph.D. courses is 20.
The credits are distributed as follows:
1. Research Mehodology:5 credits
2. Core Mathematics:10 credits
The students should take 2 optional courses of 5 credits each to get 10 credits.
3. Reading course with the Research Guide (or an optional course in lie of
it): 5 credits.
Note: The above mentioned courses with the given syllabi can also be considered as
M. Phil. courses.