Mathematics_Syllabus_3_year
... stand independently. In other words, to. pass the examination candidates will be required to obtain a minimum pass mark of 40% in each camp anent (mathematics content and the mathematics teaching methodology) before the final examination grade is worked out. The two components have separate syllabus ...
... stand independently. In other words, to. pass the examination candidates will be required to obtain a minimum pass mark of 40% in each camp anent (mathematics content and the mathematics teaching methodology) before the final examination grade is worked out. The two components have separate syllabus ...
Finite Calculus: A Tutorial - Purdue University :: Computer Science
... Now we’ll venture off onto a bit of a tangent. Because I like to keep things applied, I’d like to show that our example sum occurs in practice. It is not an equation that popped out of the aether as an interesting mathematical identity, but rather emerges during a computational analysis of Gaussian ...
... Now we’ll venture off onto a bit of a tangent. Because I like to keep things applied, I’d like to show that our example sum occurs in practice. It is not an equation that popped out of the aether as an interesting mathematical identity, but rather emerges during a computational analysis of Gaussian ...
Annotated slides Wednesday
... General formula Miscellaneous Repetitions Permutations with indistinguishable objects Exercises See also Sections 1.5 and 1.6 of Levin’s Discrete Mathematics: an open introduction. ...
... General formula Miscellaneous Repetitions Permutations with indistinguishable objects Exercises See also Sections 1.5 and 1.6 of Levin’s Discrete Mathematics: an open introduction. ...
bma105 linear algebra
... Prerequisite : consent from the advisor is required before registration. BMA420 INTRODUCTION TO TOPOLOGY elective (4 ─ 0) Topics include topological spaces, subspaces and continuity, product spaces, connectedness, compactness, separation properties, metric spaces. For examples, Tychonoff theorem, Ur ...
... Prerequisite : consent from the advisor is required before registration. BMA420 INTRODUCTION TO TOPOLOGY elective (4 ─ 0) Topics include topological spaces, subspaces and continuity, product spaces, connectedness, compactness, separation properties, metric spaces. For examples, Tychonoff theorem, Ur ...
Chapter 0
... Given a sequence hgn i that satises a given recurrence, we seek a closed form for gn in terms of n. "Algorithm" 1 Write down a single equation that expresses gn in terms of other elements of the sequence. This equation should be valid for all integers n, assuming that g−1 = g−2 = · · · = 0. 2 Multi ...
... Given a sequence hgn i that satises a given recurrence, we seek a closed form for gn in terms of n. "Algorithm" 1 Write down a single equation that expresses gn in terms of other elements of the sequence. This equation should be valid for all integers n, assuming that g−1 = g−2 = · · · = 0. 2 Multi ...
Document
... Example: Prove that there are infinitely many prime numbers Proof: Assume there are not infinitely many prime numbers, therefore they are listable, i.e. p1,p2,…,pn Consider the number q = p1p2…pn+1. q is not divisible by any of the listed primes Therefore, q is a prime. However, it was not ...
... Example: Prove that there are infinitely many prime numbers Proof: Assume there are not infinitely many prime numbers, therefore they are listable, i.e. p1,p2,…,pn Consider the number q = p1p2…pn+1. q is not divisible by any of the listed primes Therefore, q is a prime. However, it was not ...
1 slide/page
... ◦ What is {1, 2, 3}? ◦ Complementation doesn’t make sense unless there is a universe, the set of elements we want to consider. ◦ If U is the universe, S = {x|x ∈ U, x ∈ ...
... ◦ What is {1, 2, 3}? ◦ Complementation doesn’t make sense unless there is a universe, the set of elements we want to consider. ◦ If U is the universe, S = {x|x ∈ U, x ∈ ...
MATHEMATICS ADMISSIONS TEST
... A finite automaton has some finite number of states; the above automaton has three states, labelled s0 , s1 and s2 . The initial state, s0 , is indicated with an incoming arrow. The automaton receives inputs (e.g. via button presses), which might cause it to change state. In the example, the inputs ...
... A finite automaton has some finite number of states; the above automaton has three states, labelled s0 , s1 and s2 . The initial state, s0 , is indicated with an incoming arrow. The automaton receives inputs (e.g. via button presses), which might cause it to change state. In the example, the inputs ...
Set Theory Basic Concepts and Definitions The Importance of Set
... The Importance of Set Theory One striking feature of humans is their inherent need – and ability – to group objects according to specific criteria. Our prehistoric ancestors grouped tools based on their hunting needs. They eventually evolved into strict hierarchical societies where a person belonged ...
... The Importance of Set Theory One striking feature of humans is their inherent need – and ability – to group objects according to specific criteria. Our prehistoric ancestors grouped tools based on their hunting needs. They eventually evolved into strict hierarchical societies where a person belonged ...
Syllabus_Science_Mathematics_Sem-5
... Introduction, distribution function, Discrete random variable (probability mass function, discrete distribution function), Continuous random variable (probability mass function, continuous distribution function), Mathematical expectation, Expected value of function of random variable, properties of ...
... Introduction, distribution function, Discrete random variable (probability mass function, discrete distribution function), Continuous random variable (probability mass function, continuous distribution function), Mathematical expectation, Expected value of function of random variable, properties of ...
report
... Some History Hermann Weyl was a German mathematician who is also remembered for his substantial contributions to theoretical physics, mathematical physics, and philosophy. During his doctoral studies, Weyl worked under David Hilbert. He successfully proved his equidistribution theorem in 1909, and ...
... Some History Hermann Weyl was a German mathematician who is also remembered for his substantial contributions to theoretical physics, mathematical physics, and philosophy. During his doctoral studies, Weyl worked under David Hilbert. He successfully proved his equidistribution theorem in 1909, and ...
Lecture 5. Introduction to Set Theory and the Pigeonhole Principle
... In this case the set A is called the domain of f . If (a, b) ∈ f we simply write f (a) = b. With this notation, condition 1. says that for each a ∈ A, there is a b ∈ B such that f (a) = b, and condition 2. says that for each a ∈ A, there is just one b ∈ B such that f (a) = b. Taken together, the two ...
... In this case the set A is called the domain of f . If (a, b) ∈ f we simply write f (a) = b. With this notation, condition 1. says that for each a ∈ A, there is a b ∈ B such that f (a) = b, and condition 2. says that for each a ∈ A, there is just one b ∈ B such that f (a) = b. Taken together, the two ...
MS-Word version
... common set of questions and logical methods to investigate problems, and a general culture within computer science. Basically, a scientist interested in weak arithmetics knows some mathematical logic, likes Peano Arithmetic and the two Gödel Theorems, works or has been working on decision problems, ...
... common set of questions and logical methods to investigate problems, and a general culture within computer science. Basically, a scientist interested in weak arithmetics knows some mathematical logic, likes Peano Arithmetic and the two Gödel Theorems, works or has been working on decision problems, ...
4 slides/page
... ◦ number of babies: can’t have 1.2 The mathematical techniques for discrete mathematics differ from those for continuous mathematics: • counting/combinatorics ...
... ◦ number of babies: can’t have 1.2 The mathematical techniques for discrete mathematics differ from those for continuous mathematics: • counting/combinatorics ...
doc - StealthSkater
... induced from those for finite hyper-octonionic primes define the quantum states of the sub-Universe defined by given CD and sub-CDs. These phases can be assigned to any point of the 8-dimensional imbedding space M8 interpreted as hyper-octonions so that number theoretic Brahman=Atman identity or alg ...
... induced from those for finite hyper-octonionic primes define the quantum states of the sub-Universe defined by given CD and sub-CDs. These phases can be assigned to any point of the 8-dimensional imbedding space M8 interpreted as hyper-octonions so that number theoretic Brahman=Atman identity or alg ...
Practice counting problems
... In how many ways can we partition the set {1,2,3,4,5} into two disjoint subsets? ...
... In how many ways can we partition the set {1,2,3,4,5} into two disjoint subsets? ...
I.2.2.Operations on sets
... I.2.2.Operations on sets In set theory, we normally perform three fundamental operations called, the Union” ”, the intersection” ” and complement of a set A written as ( A ).The rules for the use of such operations was developed by A. De Morgan. 1. Union of sets: If we have two sets A and B , t ...
... I.2.2.Operations on sets In set theory, we normally perform three fundamental operations called, the Union” ”, the intersection” ” and complement of a set A written as ( A ).The rules for the use of such operations was developed by A. De Morgan. 1. Union of sets: If we have two sets A and B , t ...
Discrete Mathematics (2009 Spring) Basic Number Theory (n3.4gn3
... Prime Numbers De…nition (Prime) An integer p > 1 is prime i¤ it is not the product of any two integers greater than 1, p > 1 ^ :9a, b 2 N : a > 1, b > 1, ab = p. The only positive factors of a prime p are 1 and p itself. Some primes: 2, 3, 5, 7, 11, 13, De…nition (Composite) Non-prime integers great ...
... Prime Numbers De…nition (Prime) An integer p > 1 is prime i¤ it is not the product of any two integers greater than 1, p > 1 ^ :9a, b 2 N : a > 1, b > 1, ab = p. The only positive factors of a prime p are 1 and p itself. Some primes: 2, 3, 5, 7, 11, 13, De…nition (Composite) Non-prime integers great ...
Integrals Don`t Have Anything to Do with Discrete Math, Do They?
... inspiration to consider this theorem in yet another instance, this time with H graph(s) in Example 3. This application of Theorem 3 takes us down an atypical path to a commonly studied class of combinatorial objects. Derangements A derangement σ of a set S is a permutation of S with no fixed points; ...
... inspiration to consider this theorem in yet another instance, this time with H graph(s) in Example 3. This application of Theorem 3 takes us down an atypical path to a commonly studied class of combinatorial objects. Derangements A derangement σ of a set S is a permutation of S with no fixed points; ...
9649 Further Mathematics H2 for 2017
... graphical or numerical methods Approximation of roots of equations using linear interpolation and Newton-Raphson method including cases where each method fails to converge to the required root Iterations involving recurrence relations of the form x n +1 = F(x n ) including cases where the method fai ...
... graphical or numerical methods Approximation of roots of equations using linear interpolation and Newton-Raphson method including cases where each method fails to converge to the required root Iterations involving recurrence relations of the form x n +1 = F(x n ) including cases where the method fai ...
Discrete mathematics
Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous. In contrast to real numbers that have the property of varying ""smoothly"", the objects studied in discrete mathematics – such as integers, graphs, and statements in logic – do not vary smoothly in this way, but have distinct, separated values. Discrete mathematics therefore excludes topics in ""continuous mathematics"" such as calculus and analysis. Discrete objects can often be enumerated by integers. More formally, discrete mathematics has been characterized as the branch of mathematics dealing with countable sets (sets that have the same cardinality as subsets of the natural numbers, including rational numbers but not real numbers). However, there is no exact definition of the term ""discrete mathematics."" Indeed, discrete mathematics is described less by what is included than by what is excluded: continuously varying quantities and related notions.The set of objects studied in discrete mathematics can be finite or infinite. The term finite mathematics is sometimes applied to parts of the field of discrete mathematics that deals with finite sets, particularly those areas relevant to business.Research in discrete mathematics increased in the latter half of the twentieth century partly due to the development of digital computers which operate in discrete steps and store data in discrete bits. Concepts and notations from discrete mathematics are useful in studying and describing objects and problems in branches of computer science, such as computer algorithms, programming languages, cryptography, automated theorem proving, and software development. Conversely, computer implementations are significant in applying ideas from discrete mathematics to real-world problems, such as in operations research.Although the main objects of study in discrete mathematics are discrete objects, analytic methods from continuous mathematics are often employed as well.In the university curricula, ""Discrete Mathematics"" appeared in the 1980s, initially as a computer science support course; its contents were somewhat haphazard at the time. The curriculum has thereafter developed in conjunction to efforts by ACM and MAA into a course that is basically intended to develop mathematical maturity in freshmen; as such it is nowadays a prerequisite for mathematics majors in some universities as well. Some high-school-level discrete mathematics textbooks have appeared as well. At this level, discrete mathematics it is sometimes seen a preparatory course, not unlike precalculus in this respect.The Fulkerson Prize is awarded for outstanding papers in discrete mathematics.