Hi, I am wondering how good or better to say competent this program from applied math is that I would like to join this year? Here it is: Applied Mathematics ====== Year I ====== Semester 1 ----------- - Analysis 1 Real numbers. Sequences. Real functions of real variable. Continuity. Differential calculus. Indefinite integral. Certain Riemann integrals with applications. Numerical series. Degrees of rows. - Linear algebra Basic algebraic structures, vector spaces and linear mappings, base and dimension Coordinates of vectors and matrices of linear mappings, Algebra square matrix Rank matrix, determinants, systems of linear equations, matrices and reduction endomorphism, Linear and multi linear form, bilinear and quadratic forms, Euclidean vector spaces. - Introduction to mathematical logic Elementary theory, propositional calculus, predicate calculus of the first order, formal systems. - Programming 1 Computer and Programming; Computer systems; Alphabet, word, language, language processors, basic programming constructs a procedural programming language; types and terms; simple input / output; Conditional and iterative control structures, function and parameter passing; structural decomposition; modularity; Organization of the source and executable program; development of algorithms; recursion; Implementation of recursion, basic data structures: arrays, records, strings, simple algorithms numbers, strings, arrays, records, T and debugging programs. - English language English alphabet, based phonetic transcription, verbs be, have and do, members, nouns - gender, number and case, numbers, adjectives - comparation regular and irregular, basic tenses; editing texts general character.Revisiting already processed grammar; tenses, direct and indirect speech, conditional sentences, active and passive, impersonal verb forms; processing of technical texts. Semester 2 ----------- - Analysis 1 Real numbers. Sequences. Real functions of real variable. Continuity. Differential calculus. Indefinite integral. Certain Riemann integrals with applications. Numerical series. Degrees of rows. - Linear algebra Basic algebraic structures, vector spaces and linear mappings, base and dimension Coordinates of vectors and matrices of linear mappings, Algebra square matrix Rank matrix, determinants, systems of linear equations, matrices and reduction endomorphism, Linear and multi linear form, bilinear and quadratic forms, Euclidean vector spaces. - Geometry 1 Geometric concept and features of the vector in the plane and space. Vector algebra. Coordinates. The linear geometry in plane and space. Rectangular geometry in plane and space. Mapping the coordinates. Spherical geometry. - Programming 2 More advanced data types, Union, Bitwise Operators bits and fields, pointing data type; pointers and arrays; multi-dimensional arrays and arrays pointer; functions.Rad pointers to the file; standard library; command line arguments in C program; notion of time and space complexity of algorithms; A search and sort - iterative and recursive implementation; library functions search and sorting.Dynamical memory allocation, dynamic data structures: leaf, red, stack, wood.Functions to work with dynamic data structures.Formal definition of algorithms and algorithmically unsolvable problems.Owerview of programming languages and programming paradigms. ======= Year II ======= Semester 1 ---------- - Analysis 2 Metric spaces and functions of several variables. Differential calculus of functions of several variables. Implicit functions and applications in geometry. Multiple Riemann integral. Curvilinear and surface integrals and the connections between them. Functional sequences and series. Integrals that depend on a parameter. Fourier series. - Algebra 1 Elements of general algebra, Groups, finally generated Abelian groups, rings and fields, Introduction to Number Theory. - Geometry 2 Axiomatic geometry conceiving. Polygons and polyhedra. Coincidence. Continuity. Isometries of Euclidean plane and space. The similarity. Circular transformation geometry Lobachevsky. - Discrete mathematics Natural numbers, mathematical induction, the principle of the minimum number. Equivalence relations and partitions. Permutations (principle collects and products, the principle of inclusion-exclusion, Generating functions); graphs and wood (definition, planarity, the coloring); algorithmic systems and the complexity of calculation (basic notions and complexity classes); applications in cryptography (symmetric asymmetric cryptographic systems). - Introduction to computer organization and architecture 1 The history of the development of information technology. Numbering systems. The record data into the computer. Record numbers in fixed and floating point. Record integers. Recording of the Decade binary coded numbers. Arithmetic operations with numbers in fixed and floating point. Non-numerical record data. Logical base data processing. Principles of digital computers. The flow of data in a computer. The CPU, memory, input / output subsystem and devices. Detection and correction of errors. Semester 2 ---------- - Analysis 2 Metric spaces and functions of several variables. Differential calculus of functions of several variables. Implicit functions and applications in geometry. Multiple Riemann integral. Curvilinear and surface integrals and the connections between them. Functional sequences and series. Integrals that depend on a parameter. Fourier series. - Geometry 3 Parameterized curves in plane and space examples. Length of the curve. Tozija (thosis??) of curves and curves. Adjustable rapper guilty. Parameterized and desktop cases. The first and second fundamental form of the surface. Curves on the surface. The curvature of the surface. - Introduction to Numerical Mathematics Polynomial interpolation (various forms) and error of interpolacion.Numerical differentiation and integracion.Numerical methods for solving systems of linear equations and finding the inverse matrix and the determinant value (Gauss's method iteration method); methods for finding eigenvalues and vectors of regular square matrices (Jacobi-HP Householder's, LR, QR, partial problem) .Methods for solving one (method of iteration, Newton, cutters and halving) and systems of nonlinear equations (method of iteration and Newton's) .Application of exposed theory, students realize through practical exercises on computer using Matlab. - Software packages in mathematics Packages for symbolic manipulation. Numerical packages. Lots of simulation and modeling. Packages for the geometric visualization. Packages for writing mathematical text and making presentations. - Object-Oriented Programming Object-oriented paradigm. Objects, classes, inheritance. The programming language Java. Classes and inheritance in Java. Lots. Inner classes. Exceptions. Enumerated types. Generic types and methods. Reflection. Annotation. Collections. Multithreaded programming. The entrance and exit. Serialization. JavaFX. ======== Year III ======== Semester 1 ---------- - Analysis 3 Measures and Integration (General Theory), spaces of integrable functions, complex measures. - Algebra 2 Groups, Rings, Fields. (All of them) - Complex functions The field of complex numbers C. topology of the complex plane. Convergence in C. Addition formulas, trigonometric form of a complex number. Differentiable function. Cauchy-Riemann equations. Regular (holomorphic) functions. Geometric meaning of the statement. Conformal mapping. Elementary functions az + b / az + d, e z, log z, sin z, cos z and branches. Features integral. Cauchy integral theorem. Indefinite integral. Cauchy formula. Morera's theorem. Integral Cauchy type. Cauchy inequality, Liouville theorem. Cauchy-Green's formula, KIT versions, homotohopy, index, simply connected and areas with a continuous border. Features uniformly convergent sequences and series. Weierstrass theorem. Power series. Cauchy-Hadamard theorem. Abel's theorem. Teorema singleness. Taylor, Laurent series. Definition and types of isolated singularities. Count as an isolated singularity. Residuum. Application of residues to calculate real integrals. - Differential equations 1 Differential equations first order, differential equations higher order, normal systems of differential equations, analytic theory of differential equations. - Numerical Analysis 1 Numerical methods for solving systems of linear algebraic equations, numerical methods of calculating determinants and inverse matrix, numerical methods for solving the problem of eigenvalues and vectors of a matrix. - Approximation theory The mathematical apparatus. Approximation in Hilbert and Banach space. Mean square approximation. Orthogonal polynomials. The method of least squares. Fourier analysis. Discrete Fourier transformation; FFT. Wavelets. Application of signal processing and image. Uniform approximation. Semester 2 ---------- - Analysis 3 Basic principles of functional analysis, Banach and Hilbert spaces, linear operators on them and their properties. - Geometry 4 Axioms of incidence, separation and continuity and their consequences. Projective mappings. The curves of the second order. Method distance. Method trace and vanishing. Application software packages in Projective and Descriptive Geometry. - Introduction to the theory of extremal problems Quadratic functions and quadratic form of several variables. Terms of first and second order for smooth problems without restrictions. Formulation of ekstremal problems with constraints of equality and inequality type. The necessary and sufficient conditions in the form of Lagrange's principle. Convex functions of one or more variables. Kuhn-Tucker theorem. Systems of linear equations and inequalities. Theorems alternative. Duality in linear programing. Necessary condition of extremum for smooth problems with constraints of equality and inequality type. - Differential equations 2 Systems of differential equations, boundary problems, dynamic systems of equations and stability of solutions of partial differential equations. is able to apply the knowledge in applications (dynamic systems, etc.) in order to solve the problem. - Numerical Analysis 1 The interpolation functions, numerical differentiation and numerical integration, Approximation of functions, numerical methods for solving algebraic and transcendental equations and their systems. ======= Year IV ======= Semester 1 ---------- - Probability and Statistics 1 Discrete probability space. Variations, permutations, combinations. Conditional probability. Formula full probability. Independence of events. Discrete random variables. Mathematical expectation and dispersion of discrete random variables. Discrete random vectors. Independence of random variables. Binomial distribution and Bernoulli's Theorem. Čebišovljev law of large numbers. Muavr-Laplace theorem and the normal distribution. Poisson distribution. Symmetrical accidentally wander to the right. The principle of symmetry. The position of the particles after n steps in symmetric random wandering on the right. Average waiting time of return with the symmetric random wandering. Arksinusni law. Unbalanced accidentally wandering. Sigma-algebra. Axioms of probability theory. Absolutely continuous distributions (normal, uniform, exponential). Cantor singular distribution function. Decomposition of the probability distribution function. Multidimensional distribution function. Probability distribution in infinite-dimensional space. Random size (general definition). Mathematical expectation. The dispersion. Independence of random variables. Covariance and correlation coefficient. Conditional distributions. - Introduction to Theoretical Mechanics The experimental facts, examples of mechanical systems, Newton's laws, conservative fields, moving in a central field and Kepler's laws, variational principles and the Lagrange mechanics, Hamiltonian mechanics and symplectic formalism. - The equations of mathematical physics Canonization and characterization methods, partial differential equations of hyperbolic type partial differential equations of parabolic type, partial differential equations of elliptic type - Numerical analysis 2 Cauchy problem for ordinary differential equations: Analytical methods: Development of the red, Cauchy-Picard method, Newton-Kantorovich method, the method of Chaplygin, Lipetsk Area. Euler's method. Modification of Euler's method. Runge-Kutta. Multi-layered methods: Adams methods, Milne method. Runge score mistakes. Automatic selection steps, BORDER PROBLEMS for ordinary differential equations: Reduction of the Cauchy problem. Variation and projection methods. Finite difference. The concept of differential scheme. Approximation and Convergence. Solving Differential task. Schemes high accuracy. Richardson extrapolation. Sturm-Liouville problem. The finite element method, Integral Equations: Fredholm integral equations of the first and second kind. Voltera integral equations of the first and second kind. Analytical methods: Method of successive approximation, method of replacing the nucleus degenerate. Projection methods: Ric-Galerkin method, method of least squares collocation method. Methods of discretization. Methods of regularization. - Methods of mathematical programming Mathematical programming problems - definition, characteristics and classification. Linear programming. Basics of Simplex method. The theory of duality. Dual and two-phase simplex method. Analysis of efficiency simplex metode.Whole number programming. Properties and examples. Branch and bound method. Method of cutting planes. The method of branching and cutting.Nonlinear programming. Methods of optimization.Methods of unconditional and conditional optimization.Heuristic and metaheuristic methods. Local search. Simulated annealing. Tabu search. Method of variable environments. Evolutionary algorithms. Particle swarm optimization method. Optimization method of bees. Optimization method of ant colonies. Extensions of the basic concept of heuristics. Hybridization of two or more heuristics. Metaheuristics.Implementation of exact and heuristic methods for solving linear and nonlinear optimization. Application of the method implemented in the specific problems of mathematical programming and performance comparisons. Using existing software packages for optimization. - Methods of teaching Mathematics and Computing The subject methodology: Characteristic of mathematics as a science and as a school subject. The main goals of mathematics teaching (educational and pedagogical) .General method in mathematics and teaching mathematics: Observation and eksperiment.Comparison. Analysis and Synthesis. Generalization and apstraction.Froms of thinking in mathematics. Developing mathematical thinking. The principles, methods and forms of teaching mathematics. Organisation of teaching. Semester 2 ---------- - Probability and Statistics 2 Typical functions (definition, examples, properties). Teorema unity and inversion formula for characteristic functions. Convergence in probability. Borel-Kantelijev solder and almost sure convergence. Of mean convergence. Convergence in distribution (connection with characteristic functions). The relationship between the various types of convergence. Strong law of large numbers. Central limit theorem. Statistical model and the task of mathematical statistics. Population, memorial, pattern. The statistics system and a set of variations. Empirical distribution function. A sampling sample mean and dispersion and their numerical characteristics. The chi-square distribution. The joint distribution of the sampling mean and sampling dispersion of the sample from the normal distribution. T-distribution. Persistent estimates. Centered assessment. Comparison and assessment Rao-Cramer inequality. Maximum likelihood method. Confidence interval for the binomial probability distribution. Confidence interval for mathe matical expectation for a normal distribution. Confidence interal dispersion in a normal distribution. Testing statistical hypotheses. Critical power. The threshold of significance. The power of the test. Neyman-Pearson lemma. Testing hypotheses about the parameters of the normal distribution. Pearson's chi-square test. - Partial equations BASIC CONCEPTS DISTRIBUTION THEORY: Newton's potential. Distributions of slow growth. Fourier transform. Sobolev spaces. BORDER PROBLEMS FOR linear partial differential Eq (elliptic type). - Numerical Analysis 2 Partial equations of elliptic type, partial equations of elliptic type equations and hyperbolic type - Calculus of variations The formulation of the simplest problem of variational calculus and concepts of weak and strong solutions. Theorems rounding fractures. Necessary conditions of the first order: Euler equation, Weirstrass's inequality and Weirstrass-Erdmann's requirement. Euler's equation and convexity as sufficient conditions extremes. The simplest problem varijacijanog account with quadratic cost function. Necessary and sufficient conditions of the second order: Legendre and Jacobi's g½jevi conditions. Field Theory in variational calculus. The problems are reduced to the simplest problem of variational calculus. Izoperimetrijski problem in variational calculus. Problem with excerpts reda.Optimal management. - Basics of mathematical modeling What is the mathematical model. Examples of models. Basic principles in the development of the model. Models in demography and economics. Modeling of ordinary and partial differential equations. Models in Mechanics and Astronomy. Dynamic systems. Probability and stochastic models. Solving Problems in Scientific Computing Using Maple and Matlab. - Game Theory with Applications Positional games, matrix games, non-cooperative games. Games on the unit square. Cooperative games. Application. =========== Master year =========== Semester 1 ---------- - Finite Element Method The variational formulation of boundary problems. Ritz-Galerkin's method, collocation and least squares method. The final elements in one and two dimensions. The final elements of a higher order. Hierarchical finite elements. Isoparametric elements. Analysis of the error in various standards. Numerical integration and its impact on error method. Computational algorithms and software packages. - Numerical Optimization Methods 1 Differentiation in Banach spaces. Necessary and sufficient conditions of optimality. Weierstrass theorem. Methods of minimization. Methods of solving extemal tasks. - Research work 1 Semester 2 ---------- - Mathematical modeling Modeling of ordinary and partial differential equations. Models of fluid dynamics. Dynamic systems and chaotic phenomena. Models based on optimization. Estimates of the parameters in the mathematical model. Mathematical Models in Applied Mechanics. Case Studies and Projects. Practical Applied Mathematics Modelling. Parameter Estimation. - Independent research 2 The student is trained to independently prepare the graduate (master) work in the field of mathematics. - Graduate Master's Thesis The master work represents independent research student in which he meets with the methodology of research in specific areas of mathematics. After the research student prepares the final work in a form that contains the following chapters: introduction, theoretical part, results and discussion, conclusion and review literature.After that student access to defense work before the commission within which presents the results obtained by when creating work. Other electives (except for three selected) are: Combinatorial Optimization, Optimal Control, Operations Research, Selected chapters of numerical mathematics, Selected Topics of optimization, numerical optimization methods 2 or subject from another module. I would like to know how good it is to other programs (predominantly in Europe and in North America)-in sense would I get all the necessary knowledge and skills for a job later on and would I get a broad all round base in math? I've looked at programs of some universities from Europe and US and I found certain similarities, but I would like to get an opinion from somebody who has more knowledge and experience with applied math and math in general then myself. Thanks.