This document provides information about a Discrete Mathematics course. It includes:
1) Contact information for the instructor, Sherzod Turaev, and details about lecture and tutorial class times and locations.
2) Information about required and recommended textbooks.
3) An outline of the course topics to be covered each week over the semester, including fundamentals of discrete mathematics, logic, counting, relations and graphs, trees, and graph theory.
This document discusses integration by substitution. It provides examples of using substitution to evaluate various integrals involving trigonometric, exponential, and logarithmic functions. Guidelines are provided for choosing the substitution variable u. Several worked examples demonstrate how to use substitution to rewrite integrals in terms of u and then evaluate the integral. Exercises at the end provide additional practice problems for students to evaluate using integration by substitution.
1. The document discusses the history and concepts of set theory, including how it was founded by Georg Cantor and how work by Zermelo and Fraenkel led to the commonly used ZFC set of axioms.
2. Various concepts in set theory are defined, such as empty sets, singleton sets, finite and infinite sets, unions, intersections, differences, and subsets.
3. The document also discusses applications of set theory and related fields like fuzzy logic, rough set theory, and how fuzzy set theory has been applied in rock engineering characterization.
The document defines and discusses monotone sequences. A sequence {an} is defined as increasing if an < an+1, non-decreasing if an ≤ an+1, decreasing if an > an+1, and non-increasing if an ≥ an+1. Methods for determining if a sequence is monotone include the difference method, ratio method, and derivative method. Bounded and eventually monotone sequences are shown to converge according to the monotone sequence convergence theorem.
This document provides an overview of key concepts in set theory including:
- Elements, equal sets, subsets, power sets, union, intersection, difference, and complement operations on sets.
- Sets are defined as unordered collections of unique objects. Common set examples include integers, rationals, and reals.
- Key properties include elements, equal sets, subsets, empty sets, singleton sets, set-builder and extension notations, and Venn diagrams for representation.
- Operations on sets manipulate elements and include union, intersection, difference, and complement.
The document introduces complex numbers and their properties. It defines the imaginary unit i as the square root of -1. Complex numbers have both a real and imaginary part and can be added, subtracted, multiplied and divided. Powers of i rotate through the values of i, -1, -i, and 1, depending on whether the exponent is 1, 2, 3, or 4 modulo 4. Real and imaginary numbers are subsets of complex numbers.
The document discusses converse, inverse, and contrapositive statements of conditional (if-then) statements. It provides examples of converting statements to their converse, inverse, and contrapositive forms. It also discusses determining the truth value of predicates by substituting values for predicate variables.
This document discusses integration by substitution. It provides examples of using substitution to evaluate various integrals involving trigonometric, exponential, and logarithmic functions. Guidelines are provided for choosing the substitution variable u. Several worked examples demonstrate how to use substitution to rewrite integrals in terms of u and then evaluate the integral. Exercises at the end provide additional practice problems for students to evaluate using integration by substitution.
1. The document discusses the history and concepts of set theory, including how it was founded by Georg Cantor and how work by Zermelo and Fraenkel led to the commonly used ZFC set of axioms.
2. Various concepts in set theory are defined, such as empty sets, singleton sets, finite and infinite sets, unions, intersections, differences, and subsets.
3. The document also discusses applications of set theory and related fields like fuzzy logic, rough set theory, and how fuzzy set theory has been applied in rock engineering characterization.
The document defines and discusses monotone sequences. A sequence {an} is defined as increasing if an < an+1, non-decreasing if an ≤ an+1, decreasing if an > an+1, and non-increasing if an ≥ an+1. Methods for determining if a sequence is monotone include the difference method, ratio method, and derivative method. Bounded and eventually monotone sequences are shown to converge according to the monotone sequence convergence theorem.
This document provides an overview of key concepts in set theory including:
- Elements, equal sets, subsets, power sets, union, intersection, difference, and complement operations on sets.
- Sets are defined as unordered collections of unique objects. Common set examples include integers, rationals, and reals.
- Key properties include elements, equal sets, subsets, empty sets, singleton sets, set-builder and extension notations, and Venn diagrams for representation.
- Operations on sets manipulate elements and include union, intersection, difference, and complement.
The document introduces complex numbers and their properties. It defines the imaginary unit i as the square root of -1. Complex numbers have both a real and imaginary part and can be added, subtracted, multiplied and divided. Powers of i rotate through the values of i, -1, -i, and 1, depending on whether the exponent is 1, 2, 3, or 4 modulo 4. Real and imaginary numbers are subsets of complex numbers.
The document discusses converse, inverse, and contrapositive statements of conditional (if-then) statements. It provides examples of converting statements to their converse, inverse, and contrapositive forms. It also discusses determining the truth value of predicates by substituting values for predicate variables.
The document introduces complex numbers and different ways to represent them, including:
1) Imaginary numbers, represented by i, which allows for solutions to equations with "hidden roots". Complex numbers have both a real and imaginary part.
2) Polar form represents complex numbers using modulus (distance from origin) and argument (angle from positive x-axis).
3) Exponential or Euler's form uses modulus and an imaginary exponent to represent complex numbers, where the angle must be in radians.
4) Operations like addition, subtraction, multiplication and division are introduced for complex numbers, along with converting between rectangular, polar and exponential forms.
This document introduces some basic concepts in number theory, including primes, least common multiples, greatest common divisors, and modular arithmetic. It then discusses different number systems such as decimal, binary, octal, and hexadecimal. Methods are provided for converting between these different bases, including dividing or grouping bits and multiplying by the place value. Prime numbers are defined as integers greater than 1 that are only divisible by 1 and themselves. The fundamental theorem of arithmetic states that every integer can be written as a unique product of prime factors.
Unit I of the syllabus covers propositional logic and counting theory. It introduces concepts such as propositions, logical connectives like conjunction, disjunction, negation, implication and biconditional. It discusses how to represent compound statements using these connectives and their truth tables. The unit also covers topics like predicate logic, methods of proof, mathematical induction and fundamental counting principles like permutations and combinations. It aims to provide the logical foundations for discrete mathematics concepts that will be useful in computer science and information technology.
Mathematical induction is a method of proof that can be used to prove that a statement is true for all positive integers. It involves two steps: 1) proving the statement is true for the base case, usually n = 1, and 2) assuming the statement is true for an integer k and using this to prove the statement is true for k + 1. Examples are provided to demonstrate how to use mathematical induction to prove statements such as the sum of the first n positive integers equalling n(n+1)/2 and that 7n - 1 is divisible by 6 for all positive integers n.
There are 9! = 362,880 ways to seat 9 people around a round table, as the fundamental counting principle states that with 9 seats and 9 people, each person can be placed in each seat in 9 * 8 * 7 ... * 1 = 9! ways.
Content:
1- Mathematical proof (what and why)
2- Logic, basic operators
3- Using simple operators to construct any operator
4- Logical equivalence, DeMorgan’s law
5- Conditional statement (if, if and only if)
6- Arguments
The document discusses sets, relations, and functions. It begins by providing examples of well-defined and not well-defined collections to introduce the concept of a set. A set is defined as a collection of well-defined objects. Standard notations for sets are introduced. Sets can be represented using a roster method by listing elements or a set-builder form using a common property. Sets are classified as finite or infinite based on the number of elements, and other set types like the empty set and singleton set are defined. Equal, equivalent, and disjoint sets are also defined.
With vocabulary
1. The Statements, Open Sentences, and Trurth Values
2. Negation
3. Compound Statement
4. Equivalence, Tautology, Contradiction, and Contingency
5. Converse, Invers, and Contraposition
6. Making Conclusion
1) The document uses mathematical induction to prove several formulas.
2) It demonstrates proofs for formulas like 1 + 3 + 5 + ... + (2n-1) = n^2 and 2 + 4 + ... + 2n = n(n+1).
3) The proofs follow the standard structure of mathematical induction, showing the base case is true and using the induction hypothesis to show if the statement is true for n it is also true for n+1.
THE BINOMIAL THEOREM shows how to calculate a power of a binomial –
(x+ y)n -- without actually multiplying out.
For example, if we actually multiplied out the 4th power of (x + y) --
(x + y)4 = (x + y) (x + y) (x + y) (x + y)
-- then on collecting like terms we would find:
(x + y)4 = x4 + 4x3y + 6x2y2 + 4xy3 + y4 . . . . . (1)
This document provides information about sequences and series in mathematics. It defines sequences, limits of sequences, convergence and divergence of sequences, infinite series, tests to determine convergence of series like the divergence test, limit comparison test, ratio test, root test, and power series. Examples of applying these concepts to specific series are also included.
Unit 1: Topological spaces (its definition and definition of open sets)nasserfuzt
Learning Objectives:
1. To understand the definition of topology with examples
2. To know the intersection and union of topologies
3. To understand the comparison of topologies
This document presents an introduction to rules of inference. It defines an argument and valid argument. It then explains several common rules of inference like modus ponens, modus tollens, addition, and simplification. Modus ponens and modus tollens are based on tautologies that make the conclusions logically follow from the premises. It also discusses two common fallacies - affirming the conclusion and denying the hypothesis - which are not valid rules of inference because they are not based on tautologies. Examples are provided to illustrate each rule of inference and fallacy.
This document introduces the concept of sets in discrete mathematics. It defines what a set is and discusses how sets are represented and notated. It also covers basic set operations like union and intersection. Some key points include:
- A set is a collection of distinct objects, called elements.
- Sets can be represented either by listing elements within curly braces or using set-builder notation describing a common property.
- Basic set operations include union, intersection, subset, power set, and the empty set. Union combines elements in sets while intersection finds elements common to sets.
The document provides an introduction to complex numbers including:
- Combining real and imaginary numbers like 4 - 3i.
- Properties of i including i2 = -1.
- Converting complex numbers between Cartesian, polar, trigonometric and exponential forms.
- Operations on complex numbers such as addition, subtraction, multiplication and division.
- Comparing real and imaginary parts of complex numbers when solving equations.
There are three possible solutions to a system of linear equations in two variables:
One solution: the graphs intersect at a single point, giving the solution coordinates.
No solution: the graphs are parallel lines, making the system inconsistent.
Infinitely many solutions: the graphs are the same line, making the equations dependent.
The substitution method for solving systems involves: 1) solving one equation for a variable, 2) substituting into the other equation, 3) solving the new equation, and 4) back-substituting to find the remaining variable.
GROUP AND SUBGROUP PPT 20By SONU KUMAR.pptxSONU KUMAR
This document discusses key concepts in abstract algebra including groups, subgroups, normal subgroups, abelian groups, rings, and fields. It provides definitions and examples for each concept. Groups are defined as sets with a binary operation that satisfy closure, associativity, identity, and inverse properties. Subgroups are subsets of a group that are also groups. Normal subgroups are subgroups where applying the group operation to a subgroup element and any group element results in another subgroup element. Abelian groups are groups where the group operation is commutative. Rings are algebraic structures with two binary operations that satisfy properties including being abelian groups under addition and semi-groups under multiplication while satisfying distributivity. Fields are non-trivial rings where multiplication is also commutative.
1. The document outlines discrete mathematics competencies covered at different levels in the undergraduate curriculum at Saint-Petersburg Electrotechnical University.
2. Many competencies are covered in the discrete mathematics course in the first year, while others are covered in courses like mathematical logic and algorithm theory in later years.
3. LETI aims to develop additional competencies beyond the SEFI levels, such as skills in mathematical logic, graphs, algorithms, and finite state machines.
This document provides an overview of complex numbers. It defines complex numbers as numbers consisting of a real part and imaginary part written in the form a + bi. It discusses the subsets of complex numbers including real and imaginary numbers. It also covers topics such as the complex conjugate, modulus, addition, subtraction, multiplication, and division of complex numbers. Finally, it mentions applications of complex numbers in science, mathematics, engineering, and statistics.
Introduction fundamentals sets and sequences (notes)IIUM
This document provides information about a Discrete Mathematics course taught by Sherzod Turaev. It includes the instructor's contact information, class meeting times and locations, required and recommended textbooks, how the course will be assessed, and an outline of the topics to be covered each week. The course will cover fundamental discrete mathematics topics like sets, logic, counting, relations, graphs, and mathematical structures. Students will be evaluated based on homework assignments, quizzes, a midterm exam, and a final exam.
This document provides information for the Discrete Mathematics course taught by M. Narmadha to second year computer science students. It outlines the course objectives of introducing discrete mathematics concepts for computer science. It also lists various topics that will be covered in the course across four units, such as propositional logic, sets, functions, relations, algorithms, recurrence relations, graphs and trees. Finally, it provides the lecture schedule, assessment details, attendance requirements and academic calendar for the course.
The document introduces complex numbers and different ways to represent them, including:
1) Imaginary numbers, represented by i, which allows for solutions to equations with "hidden roots". Complex numbers have both a real and imaginary part.
2) Polar form represents complex numbers using modulus (distance from origin) and argument (angle from positive x-axis).
3) Exponential or Euler's form uses modulus and an imaginary exponent to represent complex numbers, where the angle must be in radians.
4) Operations like addition, subtraction, multiplication and division are introduced for complex numbers, along with converting between rectangular, polar and exponential forms.
This document introduces some basic concepts in number theory, including primes, least common multiples, greatest common divisors, and modular arithmetic. It then discusses different number systems such as decimal, binary, octal, and hexadecimal. Methods are provided for converting between these different bases, including dividing or grouping bits and multiplying by the place value. Prime numbers are defined as integers greater than 1 that are only divisible by 1 and themselves. The fundamental theorem of arithmetic states that every integer can be written as a unique product of prime factors.
Unit I of the syllabus covers propositional logic and counting theory. It introduces concepts such as propositions, logical connectives like conjunction, disjunction, negation, implication and biconditional. It discusses how to represent compound statements using these connectives and their truth tables. The unit also covers topics like predicate logic, methods of proof, mathematical induction and fundamental counting principles like permutations and combinations. It aims to provide the logical foundations for discrete mathematics concepts that will be useful in computer science and information technology.
Mathematical induction is a method of proof that can be used to prove that a statement is true for all positive integers. It involves two steps: 1) proving the statement is true for the base case, usually n = 1, and 2) assuming the statement is true for an integer k and using this to prove the statement is true for k + 1. Examples are provided to demonstrate how to use mathematical induction to prove statements such as the sum of the first n positive integers equalling n(n+1)/2 and that 7n - 1 is divisible by 6 for all positive integers n.
There are 9! = 362,880 ways to seat 9 people around a round table, as the fundamental counting principle states that with 9 seats and 9 people, each person can be placed in each seat in 9 * 8 * 7 ... * 1 = 9! ways.
Content:
1- Mathematical proof (what and why)
2- Logic, basic operators
3- Using simple operators to construct any operator
4- Logical equivalence, DeMorgan’s law
5- Conditional statement (if, if and only if)
6- Arguments
The document discusses sets, relations, and functions. It begins by providing examples of well-defined and not well-defined collections to introduce the concept of a set. A set is defined as a collection of well-defined objects. Standard notations for sets are introduced. Sets can be represented using a roster method by listing elements or a set-builder form using a common property. Sets are classified as finite or infinite based on the number of elements, and other set types like the empty set and singleton set are defined. Equal, equivalent, and disjoint sets are also defined.
With vocabulary
1. The Statements, Open Sentences, and Trurth Values
2. Negation
3. Compound Statement
4. Equivalence, Tautology, Contradiction, and Contingency
5. Converse, Invers, and Contraposition
6. Making Conclusion
1) The document uses mathematical induction to prove several formulas.
2) It demonstrates proofs for formulas like 1 + 3 + 5 + ... + (2n-1) = n^2 and 2 + 4 + ... + 2n = n(n+1).
3) The proofs follow the standard structure of mathematical induction, showing the base case is true and using the induction hypothesis to show if the statement is true for n it is also true for n+1.
THE BINOMIAL THEOREM shows how to calculate a power of a binomial –
(x+ y)n -- without actually multiplying out.
For example, if we actually multiplied out the 4th power of (x + y) --
(x + y)4 = (x + y) (x + y) (x + y) (x + y)
-- then on collecting like terms we would find:
(x + y)4 = x4 + 4x3y + 6x2y2 + 4xy3 + y4 . . . . . (1)
This document provides information about sequences and series in mathematics. It defines sequences, limits of sequences, convergence and divergence of sequences, infinite series, tests to determine convergence of series like the divergence test, limit comparison test, ratio test, root test, and power series. Examples of applying these concepts to specific series are also included.
Unit 1: Topological spaces (its definition and definition of open sets)nasserfuzt
Learning Objectives:
1. To understand the definition of topology with examples
2. To know the intersection and union of topologies
3. To understand the comparison of topologies
This document presents an introduction to rules of inference. It defines an argument and valid argument. It then explains several common rules of inference like modus ponens, modus tollens, addition, and simplification. Modus ponens and modus tollens are based on tautologies that make the conclusions logically follow from the premises. It also discusses two common fallacies - affirming the conclusion and denying the hypothesis - which are not valid rules of inference because they are not based on tautologies. Examples are provided to illustrate each rule of inference and fallacy.
This document introduces the concept of sets in discrete mathematics. It defines what a set is and discusses how sets are represented and notated. It also covers basic set operations like union and intersection. Some key points include:
- A set is a collection of distinct objects, called elements.
- Sets can be represented either by listing elements within curly braces or using set-builder notation describing a common property.
- Basic set operations include union, intersection, subset, power set, and the empty set. Union combines elements in sets while intersection finds elements common to sets.
The document provides an introduction to complex numbers including:
- Combining real and imaginary numbers like 4 - 3i.
- Properties of i including i2 = -1.
- Converting complex numbers between Cartesian, polar, trigonometric and exponential forms.
- Operations on complex numbers such as addition, subtraction, multiplication and division.
- Comparing real and imaginary parts of complex numbers when solving equations.
There are three possible solutions to a system of linear equations in two variables:
One solution: the graphs intersect at a single point, giving the solution coordinates.
No solution: the graphs are parallel lines, making the system inconsistent.
Infinitely many solutions: the graphs are the same line, making the equations dependent.
The substitution method for solving systems involves: 1) solving one equation for a variable, 2) substituting into the other equation, 3) solving the new equation, and 4) back-substituting to find the remaining variable.
GROUP AND SUBGROUP PPT 20By SONU KUMAR.pptxSONU KUMAR
This document discusses key concepts in abstract algebra including groups, subgroups, normal subgroups, abelian groups, rings, and fields. It provides definitions and examples for each concept. Groups are defined as sets with a binary operation that satisfy closure, associativity, identity, and inverse properties. Subgroups are subsets of a group that are also groups. Normal subgroups are subgroups where applying the group operation to a subgroup element and any group element results in another subgroup element. Abelian groups are groups where the group operation is commutative. Rings are algebraic structures with two binary operations that satisfy properties including being abelian groups under addition and semi-groups under multiplication while satisfying distributivity. Fields are non-trivial rings where multiplication is also commutative.
1. The document outlines discrete mathematics competencies covered at different levels in the undergraduate curriculum at Saint-Petersburg Electrotechnical University.
2. Many competencies are covered in the discrete mathematics course in the first year, while others are covered in courses like mathematical logic and algorithm theory in later years.
3. LETI aims to develop additional competencies beyond the SEFI levels, such as skills in mathematical logic, graphs, algorithms, and finite state machines.
This document provides an overview of complex numbers. It defines complex numbers as numbers consisting of a real part and imaginary part written in the form a + bi. It discusses the subsets of complex numbers including real and imaginary numbers. It also covers topics such as the complex conjugate, modulus, addition, subtraction, multiplication, and division of complex numbers. Finally, it mentions applications of complex numbers in science, mathematics, engineering, and statistics.
Introduction fundamentals sets and sequences (notes)IIUM
This document provides information about a Discrete Mathematics course taught by Sherzod Turaev. It includes the instructor's contact information, class meeting times and locations, required and recommended textbooks, how the course will be assessed, and an outline of the topics to be covered each week. The course will cover fundamental discrete mathematics topics like sets, logic, counting, relations, graphs, and mathematical structures. Students will be evaluated based on homework assignments, quizzes, a midterm exam, and a final exam.
This document provides information for the Discrete Mathematics course taught by M. Narmadha to second year computer science students. It outlines the course objectives of introducing discrete mathematics concepts for computer science. It also lists various topics that will be covered in the course across four units, such as propositional logic, sets, functions, relations, algorithms, recurrence relations, graphs and trees. Finally, it provides the lecture schedule, assessment details, attendance requirements and academic calendar for the course.
This document discusses several topics related to engineering education, including:
1. It proposes a model curriculum structure with categories of courses (mathematics/science, humanities, engineering science, etc.), number of credits, and when they should be taken.
2. It discusses emerging engineering subjects like synthetic biology, artificial intelligence, and more.
3. It addresses pedagogical issues like improving skills in teamwork, ethics, and understanding of government/economics.
4. Curriculum revision is a major task that includes updating course objectives, outcomes, syllabi, and potentially removing/adding subjects.
In summary, the document outlines models for engineering curriculum design and addresses challenges in re
This document discusses innovative practices in teaching discrete structures/mathematics and data structures to undergraduate computer science students. It describes course structures at various universities and suggests focusing discrete mathematics on fundamental concepts like logic, proofs, and counting before more advanced topics. For data structures, it recommends teaching implementation to build understanding but also focusing on usage. Projects, multimedia, and games are presented as motivating teaching techniques. Historical sources are proposed to provide context for abstract concepts.
Impending Changes in Undergraduate Curriculum sathish sak
This document discusses several topics related to engineering curriculum design including:
- Recommendations for the distribution of credits across various subject areas in the first four semesters, including mathematics, basic sciences, humanities, and engineering courses.
- Suggestions for the types of courses that should be included in the final four semesters, such as compulsory professional courses, electives, labs, projects, etc.
- Ideas for introducing more interdisciplinary subjects, undergraduate research opportunities, and focusing on areas of national need to better prepare students.
- The need to develop bridges between disciplines and teach students to work in interdisciplinary teams and learn throughout their careers.
This article discusses research on students' understanding of trigonometric functions. It finds that traditional instruction emphasizes trigonometric ratios over understanding functions. As a result, students have difficulty understanding trigonometric functions as mathematical operations that can be applied to angles. Many students cannot approximate values or reason about properties of trigonometric functions without direct computation. The article recommends instruction help students conceive of trigonometric operations as processes that take angles as inputs and map them to real number outputs.
This document provides information about the Discrete Structure course offered at MNS University of Agriculture Multan. The 3 credit hour course is offered in the 2nd semester to BSIT and BSCS students. It will be taught by Dr. Ayesha Hakim, Mr. Adnan Altaf, and Mr. Muhammad Ashad Baloch. The course aims to enable students to apply logical reasoning and understand discrete structures and their relevance to computer science. Students will be evaluated based on mid-term and final exams, assignments, and class participation. The course will cover topics like logic, sets, functions, graphs, trees, and matrices over 18 weeks.
The Teaching Of Mathematics At Senior High School In FranceXu jiakon
The document summarizes the structure of secondary education in France and reforms to mathematics education at the senior high school level. It discusses the challenges facing senior high school mathematics education that motivated reforms in 2000, including the massification of education and adapting to changes in mathematics and social needs. The reforms aimed to increase the role of statistics, probability, technology, and links to other disciplines. They faced difficulties in implementation due to time constraints and gaps in teachers' training. Current projects consider more flexible curricula and connections between mathematics and computer science.
Scheme g third semester (co,cm,cd,if, cw)anita bodke
This document outlines the teaching and examination scheme for the third semester of various diploma programs. It includes:
1. The subject Data Structure Using 'C' which has 4 hours of theory and 4 hours of practical classes per week. It will be examined through a theory paper worth 100 marks, a practical exam of 50 marks, and internal assessment of 25 marks.
2. Details of the Applied Mathematics subject including its objectives, learning structure, theory topics and contents across various engineering programs for the third semester.
3. Excerpts from documents providing more context on the Data Structure Using 'C' and Applied Mathematics subjects, including their objectives, importance, and learning outcomes for students.
The document provides course structures and syllabi for the first year B.Tech program under the R20 regulations at Jawaharlal Nehru Technological University Anantapur. It includes details of the induction program in semester 0 and the courses offered in semesters 1 and 2 for the Computer Science Engineering (Artificial Intelligence) program. The courses cover topics such as linear algebra, calculus, chemistry, C programming, data structures, physics, communication skills, and engineering workshops and laboratories. The document provides information on course codes, categories, credits, and learning outcomes for each course.
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.
R15 regulations i b.tech - isem.pdf 974772Dandu Srinivas
This document provides course structures for various B.Tech programs offered at Jawaharlal Nehru Technological University Anantapur.
It includes the course codes, subjects, theory/tutorial/lab hours and credits for the first semester of programs like CSE/EEE/CE and ECE/ME/EIE/IT. The courses include subjects like Functional English, Mathematics, Computer Programming, Engineering Chemistry/Physics, Environmental Studies etc.
It also provides details about the internal assessment and end examination patterns for subjects like Engineering Drawing. The document gives the framework of subjects and their credits that will be covered in the first semester of different engineering branches at the university.
MetaMath and MathGeAr Projects: Students' Perceptions of Mathematics in Engin...Mohamed El-Demerdash
This research aims at studying engineering students’ perceptions of their mathematics courses. We present the methodology of data collection, the main themes that the questionnaire investigates and the results. The population on which we base this study are partners in two Tempus projects, MetaMath in Russia and MathGeAr in Georgia and Armenia.
Pedro Lealdino Filho, Christian Mercat, Mohamed El-Demerdash. MetaMath and MathGeAr Projects: Students’ perceptions of mathematics in engineering courses. In E. Nardi, C. Winsløw & T. Hausberger (Eds.), Proceedings of the First Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2016, 31 March-2 April 2016), (pp. 527-528). Montpellier, France: University of Montpellier.
Outcomes based teaching learning plan (obtlp) trigonometryElton John Embodo
This document outlines an outcomes-based teaching and learning plan for a Trigonometry course at GOV. ALFONSO D. TAN COLLEGE. The course aims to provide students with an understanding of trigonometric functions, identities, and their applications. Over 14 weeks, students will learn about right triangles, oblique triangles, trigonometric identities, and complex numbers. Assessment will include quizzes, performance tasks, exams, and group activities. The course is intended to help students achieve the program learning outcomes of the Bachelor of Secondary Education - Math program.
This book provides a unique approach to making mathematics education research on addition, subtraction, and number concepts accessible to teachers. It reveals students' thought processes through annotated student work samples and teaching experiences. The book aims to help teachers modify lessons and improve student learning in primary grades. Key features include a focus on student work, research from the Ongoing Assessment Project, connections to Common Core standards, and questions to analyze student thinking. The goal is to bridge the gap between research findings and practical classroom application to support student understanding of foundational additive concepts.
OntoMаthPro Ontology: A Linked Data Hub for MathematicsAlik Kirillovich
O. Nevzorova, N. Zhiltsov, A. Kirillovich, E. Lipachev. OntoMathPro Ontology: A Linked Data Hub for Mathematics // Knowledge Engineering and the Semantic Web. 5th International Conference, Proceedings. — Communications in Computer and Information Science, Vol. 468 — Springer International Publishing — 2014 — pp. 105-119.
This document summarizes a presentation about using spreadsheets, particularly Excel, to facilitate mathematics education. It discusses how spreadsheets can help students understand mathematical concepts from a young age by allowing them to recognize patterns, formulate relationships, and test conjectures quickly. The presentation provides examples of how spreadsheets have been used successfully in classrooms and cites research supporting their benefits for transitioning students from arithmetic to algebraic reasoning. It also outlines other ways spreadsheets can engage students, such as through conditional formatting and solving games like Sudoku.
A Survey of Mathematics Education Technology Dissertation Scope and Quality ...Crystal Sanchez
This dissertation survey examined 480 mathematics education technology dissertations from 1968 to 2009. It found that dissertation studies earned an average of 64.4% of possible quality points across all methodologies, higher than comparable journal studies which averaged 47.2%. The dissertation studies focused most on calculators and software, and outcomes related to student achievement and attitudes. However, the quality of theoretical connections, research design descriptions, and validity/reliability reporting in dissertations was inconsistent. Improving these areas could increase dissertation and research quality in this field.
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.
Similar to Introduction fundamentals sets and sequences (20)
1. Create an account on 000webhost.com and choose a free subdomain as the domain name for your project website.
2. After registering, open the activation email and sign in to the 000webhost control panel using your credentials.
3. Use an FTP client like FileZilla to connect to the 000webhost server using the FTP details, and upload all project files to the public_html folder.
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This document discusses multimedia and its applications. It defines multimedia as a combination of different media types, and notes that multimedia becomes interactive when users can control elements. It then describes common applications of multimedia in business, education, homes, and public spaces. Finally, it discusses methods of delivering multimedia, including via CD-ROM, DVD, and virtual reality.
The Kreydle Internship Program provides a 5-week training program for interns to learn multimedia skills like video production, photography, and presentation design. Interns are mentored and work on projects aligned with quarterly objectives and key results. The program teaches skills in areas like storyboarding, recording, editing, and teaches interns to create an engaging LinkedIn profile and internship experience video. Interns learn our company culture of learning, sharing, and accountability.
PHP scripts contain PHP code interspersed with HTML. PHP code is contained within opening <?php and closing ?> tags and is interpreted by the Zend engine before the page is sent to the browser. There are different styles of PHP tags like XML, short open, script, and ASP styles. PHP supports core data types like integers, floats, strings, booleans and other special types. Variables in PHP begin with a $ sign and have a name, value, and type. Constants are values that cannot change during script execution and are defined using the define() function.
The document provides requirements for creating an entity relationship diagram (ERD) for a National Hockey League database. It specifies that the ERD should include entities for teams, players, games and their attributes and relationships. A sample ERD is provided that models teams as having a name, city, coach and captain, players as belonging to teams and having attributes, and games as connecting two teams with a date and score.
This document provides instructions for a group assignment on data structures and algorithms. It contains 4 questions:
1. Determine the output of sample C++ code that performs a binary search on an array to find a given input value.
2. Represent -8, 8, and 0.3125 in their corresponding 4-bit signed integer and 16-bit floating point binary formats or explain why it is not possible.
3. Circle properties that describe arrays as a data structure and explain the selection. The properties are basic/compound, static/dynamic, and linear/non-linear.
4. For a 3D array stored in column-wise format: a) calculate the address of a given element, and b
Tutorial import n auto pilot blogspot friendly seoIIUM
Teks ini memberikan tutorial cara mengimpor konten blog dan mengotomatisasi pembaharuan blog di Blogspot tanpa perangkat lunak, dengan memanfaatkan fitur impor RSS dan otomatisasi IFTTT. Beberapa langkah kuncinya adalah menemukan blog target melalui pencarian Google, mengambil RSS feed-nya, mengimpor konten ke blog sendiri di Blogspot, lalu mengatur IFTTT untuk secara otomatis mengambil setiap update dari blog target. Penulis menegaskan
Visual scenes are composed of objects and surfaces arranged in a meaningful spatial layout. Perceiving scenes involves understanding the overall meaning or "gist" of the scene from a single glance, even though details may not be perceived or remembered. Scene perception relies heavily on global spatial layout and statistical regularities rather than individual object recognition. The brain reconstructs scenes using memory, knowledge and expectations which can lead to errors like boundary extension or change blindness where details are missed or falsely remembered.
This document discusses HTML forms and how they interact with PHP. It begins by explaining that forms are used to collect and process user input data on websites. It then covers key topics like the structure and elements of an HTML form, how forms send data to a server via GET and POST methods, and how PHP can then access and use the submitted form data on the server-side. Examples are provided throughout to illustrate form markup, form submission handling in PHP, and how data is transmitted between the client and server.
This document appears to be notes from a data structures and algorithms course, listing time complexities of various algorithms. It includes big O notations for operations that take constant, linear, quadratic, and cubic time, as well as square root and log time. Code examples are used only to explain algorithms at a high level without specific programming syntax.
This document contains multiple choice and short answer questions about data structures such as arrays, linked lists, stacks, queues, and trees. The multiple choice questions test knowledge of the basic properties and applications of these data structures. The short answer questions involve coding examples using recursion, stacks, queues, and linked lists to solve problems.
The document discusses priority queues and binary heaps. It explains that priority queues store tasks based on priority level and ensure the highest priority task is at the head of the queue. Binary heaps are the underlying data structure used to implement priority queues. The key operations on a binary heap are insert and deleteMin. Insert involves adding an element and percolating it up the heap, while deleteMin removes the minimum element and percolates the replacement down. Both operations have O(log n) time complexity. The document provides examples and pseudocode for building a heap from a list of elements in O(n) time using a buildHeap method.
This document provides guidelines for preparing final year project reports at the Kulliyyah of Engineering at the International Islamic University Malaysia. It outlines requirements for report formatting, including paper size and type, font styles and sizes, margins, page numbering, headings, paragraphs, and binding. It also describes the required contents and order, including a cover page, title page, abstract, acknowledgements, table of contents, body of the text organized into chapters, and references. The body of the text must include chapters on introduction, theoretical background or literature review, methodology, presentation of results, discussion, and conclusions.
To use Edpuzzle, students should go to edpuzzle.com, log in or create an account using their Google account or by creating a new account, and update their profile name to their matrix number. Students then join their class by entering the given class code provided by their teacher.
The document discusses the benefits of exercise for mental health. Regular physical activity can help reduce anxiety and depression and improve mood and cognitive function. Exercise causes chemical changes in the brain that may help protect against developing mental illness and improve symptoms for those who already suffer from conditions like anxiety and depression.
The document discusses the benefits of exercise for mental health. Regular physical activity can help reduce anxiety and depression and improve mood and cognitive functioning. Exercise causes chemical changes in the brain that may help protect against mental illness and improve symptoms.
This document outlines requirements for a group assignment to create a simple website using HTML. Students must create a web hosting account and develop a main page with two sections - a 20% wide left menu and 80% wide right display area. The menu should include hyperlinks to individual member pages on the right. Each member page should include that person's photo, name, student ID, and email in an HTML table. Students should save all files in a compressed folder named after their group, submit via the learning platform, and publish the complete site online. The assignment has guidelines around group size, submissions, and maintaining the published site.
This document provides an overview of AVL tree rotations, including left, right, left-right and right-left rotations. It explains how each rotation works by restructuring the nodes and subtrees. Situations requiring each type of rotation are demonstrated through examples. Rules for determining which rotation to use based on whether the tree is left or right heavy and the balance of related subtrees are also outlined. The document aims to explain rotations, when they are needed to rebalance the tree, and how to identify the appropriate rotation to apply in different unbalanced scenarios.
The document discusses graphs and graph algorithms. It defines graph terminology like vertices, edges, adjacency matrix, and adjacency list representations of graphs. It then explains the breadth-first search (BFS) algorithm through an example, showing how BFS visits vertices level-by-level starting from the source vertex. BFS uses a queue and predecessor array to keep track of the shortest paths found. The document also briefly introduces depth-first search (DFS) and shows the beginning of an example DFS.
Temple of Asclepius in Thrace. Excavation resultsKrassimira Luka
The temple and the sanctuary around were dedicated to Asklepios Zmidrenus. This name has been known since 1875 when an inscription dedicated to him was discovered in Rome. The inscription is dated in 227 AD and was left by soldiers originating from the city of Philippopolis (modern Plovdiv).
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إضغ بين إيديكم من أقوى الملازم التي صممتها
ملزمة تشريح الجهاز الهيكلي (نظري 3)
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تتميز هذهِ الملزمة بعِدة مُميزات :
1- مُترجمة ترجمة تُناسب جميع المستويات
2- تحتوي على 78 رسم توضيحي لكل كلمة موجودة بالملزمة (لكل كلمة !!!!)
#فهم_ماكو_درخ
3- دقة الكتابة والصور عالية جداً جداً جداً
4- هُنالك بعض المعلومات تم توضيحها بشكل تفصيلي جداً (تُعتبر لدى الطالب أو الطالبة بإنها معلومات مُبهمة ومع ذلك تم توضيح هذهِ المعلومات المُبهمة بشكل تفصيلي جداً
5- الملزمة تشرح نفسها ب نفسها بس تكلك تعال اقراني
6- تحتوي الملزمة في اول سلايد على خارطة تتضمن جميع تفرُعات معلومات الجهاز الهيكلي المذكورة في هذهِ الملزمة
واخيراً هذهِ الملزمة حلالٌ عليكم وإتمنى منكم إن تدعولي بالخير والصحة والعافية فقط
كل التوفيق زملائي وزميلاتي ، زميلكم محمد الذهبي 💊💊
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Gender and Mental Health - Counselling and Family Therapy Applications and In...PsychoTech Services
A proprietary approach developed by bringing together the best of learning theories from Psychology, design principles from the world of visualization, and pedagogical methods from over a decade of training experience, that enables you to: Learn better, faster!
How Barcodes Can Be Leveraged Within Odoo 17Celine George
In this presentation, we will explore how barcodes can be leveraged within Odoo 17 to streamline our manufacturing processes. We will cover the configuration steps, how to utilize barcodes in different manufacturing scenarios, and the overall benefits of implementing this technology.
This document provides an overview of wound healing, its functions, stages, mechanisms, factors affecting it, and complications.
A wound is a break in the integrity of the skin or tissues, which may be associated with disruption of the structure and function.
Healing is the body’s response to injury in an attempt to restore normal structure and functions.
Healing can occur in two ways: Regeneration and Repair
There are 4 phases of wound healing: hemostasis, inflammation, proliferation, and remodeling. This document also describes the mechanism of wound healing. Factors that affect healing include infection, uncontrolled diabetes, poor nutrition, age, anemia, the presence of foreign bodies, etc.
Complications of wound healing like infection, hyperpigmentation of scar, contractures, and keloid formation.