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Mathematics And Computing
Computing means an activity to achieve a goal and benefiting from the computers.Computing comprises with the development of computer
hardware, the use of computer applications, and the development of computer software.
Computing is the ultimate mental amplifier we can say.Automatic computing radically changes how humans solve problems, and even the kinds of problems we just imagine to solve.
All of the most exciting and important technologies, arts, and sciences are driven by computing.
Computing can be approach by three perspectives i.e.,
Models of computation are :-
- -Deterministic computation
- -Rigid models
- -Pointer machines
Dterministic computation consists of events represented as graphs with causal edges.Rigid computations has a node parameters called
cell or location with structured edges.Cellular Automata is a parallel rigid model.All types of machines or the model of computation will compute only if it is computed by the TM (Turing Machine).
Some major computing sub-disciplines are as follows:-
Computational mathematics comprises of algorithms, symbolic computations and numerical methods. It enhances a student’s research, inquiry and analytical thinking abilities. In this computing, Partial differential equations are used to solve realistic industrial problems. These equations consists of following three classes:
- Elliptic: it involves Poisson equation.
- Parabolic: it involves heat or diffusion equation.
- Hyperbolic: it involves transport equation.
Computational linear algebra is a major part of mathematics computing. Linux platform is used for scientific computing. Julia programming language is also used to do computing. Discrete mathematics methods is the main tool for a computer scientist.
Computational maths identifies and applies concepts of set theory, binary relations, logic, proof techniques, arithmetic, graphs and trees, counting methods and probability. It provides convincing arguments by analyzing mathematical proofs and discriminates between valid and fallacious arguments.
It uses skills to investigate and solve a variety of discrete mathematical problems. Some of mathematical applications of computing are digital computers and analog computers. It uses mathematical models for business and finance, science, medicine, weather forecasting, engineering. Some of the possible research interests in this are listed as:
- Algorithms for parallel computers
- Direct and inverse scattering
- Three -dimensional tumor growth and water waves models applications
- Adaptive methods for elliptic problems
- Adaptive methods parabolic problems
- Iterative methods
- Numerical methods for optimization problems
- Time-stepping algorithms
- Parallel-time algorithms
- Computational approach to PDEs
- Computational approach to boundary integral equations
- Quasi Monte-Carlo methods
- High dimensional integration
Computing : Principles of logic, set theory, induction, and algebraic structures with applications to computing; finite state machines; and limits of computability, enumeration & discrete probability , applications of randomness to computing; polynomial-time versus NP; and NP-completeness
Some of the homework help topics include:
- Definition of a matrix ,Matrix addition ,Scalar multiplication of a matrix ,Matrix multiplication and its properties
- Column and row matrices (vectors) ,Equality of matrices
- Square, diagonal, identity, null, symmetric, skew-symmetric, and triangular ,matrices.
- Orthogonal matrix, invertible matrix and transpose of a matrix ,Determinants of matrices
Mathematics And Computing Questions help :
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Help for complex topics like:
- determinants , Singular and non-singular matrices , adjoint of a square matrix and its properties ,Finding inverse of a matrix ,Systems of linear equations ,Sequences and Series
Define a sequence
- Identify different types of sequences ,Define the different types of limits of sequences
- Identify properties of sequences and use them to evaluate limits of sequences
- Define a series ,Identify convergent series and divergent series ,Identify tests for convergence and apply them to determine whether a series is convergent or not
- Define a power series ,Identify properties of power series ,Sequences ,Definition of a sequence ,Convergent and divergent sequences
- Limits of a sequence ,Elementary properties of limits ,Monotonic sequences ,Bounded sequences
- Relationship between monotonicity, boundedness ,Infinite Series ,Definition ,Convergence and Divergence ,Fundamental facts about infinite series ,Power Series ,Fundamental facts about power series
- Taylor and Maclaurin Series ,Vectors ,Distinguish between vectors and scalars ,Use vector concepts ,Apply vector theory in geometry
- vector and a scalar ,Equality of vectors ,Geometric representation of a vector ,Magnitude of a vector
- Unit vector and null vector ,Multiplication of a vector by a scalar ,Vector addition and subtraction ,Position vectors ,Vectors in a plane and in 3-dimensional space
- angle between two vectors ,The Ratio Theorem ,Scalar product, vector product, and their properties.
- Differentiation and Integration, Evaluate limits, Differentiate elementary functions, Solve real world problems using differentiation, Integrate standard functions, Find the area under a curve using integration
- Differentiation, Definition, Properties and examples, Higher order derivatives, Finding limits using L’Hospital’s Rule, Integration, Integration as the inverse of differentiation (the indefinite integral)
- Integration of standard functions (ex, log x, sin x, cos x, tan x, sec x, cosec, x, cot x),Techniques of integration, Properties of integration, Area under a curve (the definite integral), Basic Statistics
- Discrete probability distributions, Binomial probability distribution, the Poisson probability distribution, Use and interpret some continuous probability distributions such as the, Uniform probability distribution
- Normal probability distribution, the, Exponential probability distribution, Identify properties of the Normal probability distribution, Compute normal probabilities using standard normal tables, Convert a random variable to a standard normal random variable
- Use the normal probability distribution to approximate binomial, probabilities, Random variables, Discrete random variables Continuous random variables Probability distribution of a discrete random variable
- Mean and Variance ,Binomial probability distribution,Poisson probability distribution, Probability distribution of a continuous random variable, Mean and Variance, Uniform probability distribution
- Normal probability distribution, Normal approximation of the Binomial distribution, The Exponential distribution
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Topics like Application to Sturm-Liouville problem and approximations & the assignment help on these topics is really helpful if you are struggling with the complex problems.