EPT
Is there anyone who can recommend some books for my first semester (second year) of my Bsc Mathematics, i want to do some reading up before i start the second year in October, here are the module names and descriptions:Statistical Inference I
This module builds on MAT-10028 and illustrates how statistical theory is put into practice in a variety of hypothesis testing situations. The topics covered are: moment generating functions, bivariate distributions, distributions of functions of random variables, sampling theory, properties of point estimators, maximum likelihood, method of moments, interval estimation, hypothesis testing, Neyman-Pearson lemma, and some parametric and nonparametric tests.
Aims:
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Manipulate and derive properties of one and two-dimensional random variables, including moment generating functions, conditional and marginal distributions, distribution of functions of random variables, sampling theory and central limit theory (1, 2).
Derive and use: properties of point estimators, the method of maximum likelihood, the method of moments, methods for comparing point estimators, the Cramer-Rao Inequality and confidence intervals (1, 2).
Carry out statistical hypothesis tests, derive and use some parametric and nonparametric methods for carrying out common inferential tasks, apply the Neyman-Pearson Lemma in various circumstances (1, 2).
Derive and use: properties of point estimators, the method of maximum likelihood, the method of moments, methods for comparing point estimators, the Cramer-Rao Inequality and confidence intervals (1, 2).
Carry out statistical hypothesis tests, derive and use some parametric and nonparametric methods for carrying out common inferential tasks, apply the Neyman-Pearson Lemma in various circumstances (1, 2).
Operational Research II
The module presents a wide variety of techniques for solving quantitative problems arising in management and everyday life. The topics include: the transportation problem, dynamic programming, the Travelling Salesman Problem, scheduling, reliability, replacement and inventory models.
Aims:
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Apply a collection of standard Operational Research techniques and algorithms to deterministic problems, including the Transportation Problem, dynamic programming, scheduling, the Travelling Salesman Problem and inventory (1, 2).
Apply a collection of standard Operational Research techniques and algorithms to stochastic problems, including reliability and replacement (1, 2).
Explain the motivation for heuristics in problem-solving (1, 2).
Explain some of the issues involved in modelling organizational problems (1, 2).
Apply a collection of standard Operational Research techniques and algorithms to stochastic problems, including reliability and replacement (1, 2).
Explain the motivation for heuristics in problem-solving (1, 2).
Explain some of the issues involved in modelling organizational problems (1, 2).
Differential Equations
This module focuses on methods for solving ordinary differential equations. The topics include: solutions to first-order equations, higher order linear equations, power series methods, graphical aspects of differential equations, Fourier series and Laplace transforms.
Aims:
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Solve first order variable-separable, linear and exact ordinary differential equations (1, 2).
Solve second order ordinary differential equations using a variety of methods, including variation of parameters and power series methods (1, 2).
Apply methods for solving first and second order equations to solve various physical problems (1, 2).
Interpret the behaviour of solutions of ordinary differential equations through the use of phase plane analysis (1, 2).
Calculate Fourier series and derive results concerning such series (1, 2).
Solve ordinary differential equations through the use of Fourier series (1, 2).
Calculate the Laplace transform of various functions and derive some if its properties (1, 2).
Use Laplace transforms to solve ordinary differential equations (1, 2).
Solve second order ordinary differential equations using a variety of methods, including variation of parameters and power series methods (1, 2).
Apply methods for solving first and second order equations to solve various physical problems (1, 2).
Interpret the behaviour of solutions of ordinary differential equations through the use of phase plane analysis (1, 2).
Calculate Fourier series and derive results concerning such series (1, 2).
Solve ordinary differential equations through the use of Fourier series (1, 2).
Calculate the Laplace transform of various functions and derive some if its properties (1, 2).
Use Laplace transforms to solve ordinary differential equations (1, 2).
Analysis and Abstract Algebra
This module builds upon the first year analysis module in order to develop a rigorous theory of functions of a real variable, and introduces abstraction in mathematics through the study of abstract algebra. The module includes: limits of functions of a real variable, continuity, differentiation and Riemann integration; equivalence relations, elementary group theory, applications to number theory, modulo arithmetic, and an introduction to rings and fields.
Aims:
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Derive and apply properties of continuous functions, including the combination theorem, the composite rule, the intermediate value theorem and the boundedness theorem (1, 2).
Derive and apply properties of the derivative of a function, including rules for differentiation, maxima and minima, Rolle&©s Theorem, mean value theorems, L&©Hopital&©s rule and Taylor&©s Theorem (1, 2).
Derive and apply properties of the Riemann integral (1, 2).
Prove whether or not a given structure is a group or subgroup (1, 2).
Derive and derive basic properties of groups, including the order of a group, the period of an element, cyclic groups, cosets and Lagrange&©s Theorem (1, 2).
Derive and apply basic properties of group homomorphisms and isomorphisms (1, 2).
Derive and apply results in number theory, including Euclid&©s algorithm, properties of prime numbers and modular arithmetic, and apply group theory in number theory (1, 2).
Derive and apply properties of the derivative of a function, including rules for differentiation, maxima and minima, Rolle&©s Theorem, mean value theorems, L&©Hopital&©s rule and Taylor&©s Theorem (1, 2).
Derive and apply properties of the Riemann integral (1, 2).
Prove whether or not a given structure is a group or subgroup (1, 2).
Derive and derive basic properties of groups, including the order of a group, the period of an element, cyclic groups, cosets and Lagrange&©s Theorem (1, 2).
Derive and apply basic properties of group homomorphisms and isomorphisms (1, 2).
Derive and apply results in number theory, including Euclid&©s algorithm, properties of prime numbers and modular arithmetic, and apply group theory in number theory (1, 2).
Thanks
