Bachelor of Science in Mathematics

This course covers foundations of probability theory, combinatorial and counting methods, conditional probability, random variables, discrete and continuous distributions, expectation, moment generating functions, multivariate distributions, variable transformations, the Law of Large Numbers and the Central Limit Theorem. Prerequisite: MATH 162 Calculus II.

Course learning outcomes
1. Use basic counting techniques (multiplication rule, combinations, and permutations) to compute conditional probabilities directly and using Bayes' theorem and check for independence of events.
2. Introduce random variables and work with discrete and continuous random variables. In particular, understand the basic properties of Bernoulli, binomial, geometric Poisson distributions, uniform, Gamma and exponential, normal distribution and compute the central limit theorem.
3. Be able to compute the expectation, variance, covariance and correlation between jointly distributed variables, Moment generating functions, Transformation of random variables and the computation of order statistics.
4. Apply knowledge of probability to solve problems from the field of electronic, electrical and communications of applicable nature, falling in both discrete and continuous domain.

This course covers modular arithmetic, permutations, group theory through the isomorphism theorems and Sylow theorems, ring theory through the notions of prime and maximal ideals, factorization domains and classification of groups of small orders.

Course learning outcomes
1. Identify the given mathematical structure as a binary structure, a group, or a ring and classical groups including permutation groups; (PLO1).
2. Describe basic concepts related to groups and rings such as normal subgroups, left and right cosets, factor groups, Lagrange’s theorem, integral domains, rings with or without unity, and fields; (PLO1, 7).
3. Demonstrate the use of homomorphisms and isomorphisms in the group/ring/field settings.
4. Understand an ideal of a ring and describe its role in the study of ring properties, including the role of prime and maximal ideals, and that of factor rings.
5. Describe the notions of field extensions and finite fields.

The course starts where Probability ends and considers point estimation, method of moments, maximum likelihood estimation, unbiasedness, consistency, sampling distributions, confidence intervals, hypothesis testing, power of tests. Categorical data inference may be covered if time permits.

Course learning outcomes
1. Understand the difference between probability and likelihood functions, and compute the maximum likelihood estimate for a model parameter.
2. Compute confidence intervals for parameter estimates.
3. Use null hypothesis significance testing to test the significance of results and compute the p-value for these tests.
4. Apply specific significance tests including, z-test, t-test (one and two samples), and chi-squared test.

This course is designed to teach students basic skills that are essential in research work in mathematical sciences. Specific topics include: preparing scientific manuscripts and scientific reports using modern document preparation system LaTeX along with BibTeX and packages for creating professional graphics; preparing technical oral presentations using LaTeX and PowerPoint; efficient literature search and tools for literature review; gathering and critical evaluation of scientific information; characteristics of good research; science ethics; research funding; research proposals; bibliometrics and scientometrics; publication process in peer-reviewed journals; dissemination of research results. Along with the general concepts relevant to those topics, the students will learn how to explore research opportunities in the general mathematical sciences. Also, students will acquire skills useful for preparing resumes and job applications. The regular classes will be enriched by computer laboratory sessions and professional presentations of on-going research in the Math Dept and invited talks.

Course learning outcomes
1. Solve numerically mathematical problems (including root finding, interpolation, integration, differentiation, and ordinary differential equations).
2. Implement numerical algorithms using a programming language, i.e., Matlab.
3. Apply the fundamental principles of mathematical approximations and the concept of approximations errors.
4. Apply the concept of forward and backward errors.
5. Analyze approximation errors and construct some bounds of errors.
6. Perform basic convergence analysis of an approximation method.

This course conducts a careful treatment of the theoretical aspects of the calculus of functions of a real variable, including the real number system, the topology of the real line, open and closed sets, compactness, sequences and their limits. The course proceeds to cover series, absolute convergence, series of functions, and continuity. As time permits, derivatives may be covered as well. Prerequisite: MATH 263 Calculus III.

Course learning outcomes
1. Use properties of compact, finite, countable, and connected sets to prove theorems.
2. Apply the lemmas and theorems about convergent sequences and series.
3. Employ definitions and theorems about real-valued functions and their proofs.
4. Employ the definition derivative of a function and produce the related theorems.
5. Apply the definition of the Riemann integration and discuss integrable functions and inequalities involving integrals.

This course covers transcendental functions, advanced integration techniques, indeterminate forms, improper integrals, area and arc length in polar coordinates, infinite series, power series and Taylor’s theorem.

Course learning outcomes
1. Integrate functions whose antiderivative is given by elementary functions.
2. Use integrals in a variety of area and volume computations.
3. Solve first order differential equations by separation of variables or the method of integrating factors.
4. Analyze the convergence of series, which are either absolutely convergent or alternating.
5. Know the most usual Maclaurin series expansions and their intervals of convergence, together with how to derive them.
6. Work with curves in parametric form, especially polar coordinates.
7. Identify types of conic from their equation in Cartesian or polar coordinates.

Calculus III is a third calculus course for students who have been introduced to the basic ideas of differential and integral calculus. Over the course the following topics will be studied: Chapter 11 (Three-dimensional space; vectors) Chapter 12 (Vector-valued functions) Chapter 13 (Partial derivatives) Chapter 14 (Multiple integrals) Chapter 15 (Topics in Vector Calculus).

Course learning outcomes
1. Compute limits, derivatives, and integrals of multivariate and vector-valued functions.
2. Explain geometrical meanings of various concepts.
3. Apply Green’s and Stokes theorems in simple settings.
4. Examine simple real-world extreme value problems.
5. Apply transform rules for change of coordinates.

This one-semester course is intended for mathematics, engineering and science students. It introduces students to the fundamental concepts of linear algebra. The course primarily deals with two mathematical objects: matrix and vector, and covers topics such as solutions of systems of linear equations, properties of invertible matrices, linear transformation, determinant, eigenvalues and eigenvectors, vector spaces and subspaces, linear independence, basis, coordinates, inner product, norm, orthogonal basis, similarity, and quadratic forms.

Course learning outcomes
1. Employ row reduction algorithm to solve systems of linear equations.
2. Understand basic matrix algebra and construct linear problems in the matrix forms.
3. Implement the basic theory of finite dimensional vector spaces and related concepts such as subspaces, basis, and linear transformations; Gram-Schmidt process.
4. Solve eigenvalue problems and apply matrix diagonalization procedures.

This course is a one-semester course intended for students majoring in Mathematics or Computer Science. It introduces the students to the fundamental concepts of mathematical reasoning. The main themes of the course are logic and proof, induction and recursion, discrete structures, set theory, combinatorics, algorithms, graph theory, and their applications. The students will learn how to formulate precise mathematical statements. The course also explores several common proof techniques and exposes the students to learning how to write mathematical proofs.

Course learning outcomes
1. Describe and analyze logical expressions.
2. Understand the elementary set theory.
3. Produce elementary mathematical proofs using different methods of proof.
4. Solve simple problems related to number theory, combinatorics, and graph theory.

This is a one-semester course intended for mathematics, engineering, and science students. It covers first order differential equations; mathematical models and numerical methods; linear systems and matrices; higher-order linear differential equations; linear systems of differential equations; and Laplace transform methods.

Course learning outcomes
1. Classify differential equations and learn basic concept related to ordinary differential equations.
2. Solve linear and some simple nonlinear ordinary differential equations using different solution techniques.
3. Solve systems of first order linear ordinary differential equations.
4. Describe the general behavior of the solutions to differential equations and systems of first order linear ordinary differential equations.
5. Model simple real-world problems using ordinary differential equations.
6. Employ Laplace transform for linear ordinary initial value problems.

This course is a one-semester course intended for mathematics, computer science students. This course will cover the fundamental concepts of Graph Theory: simple graphs, digraphs, Eulerian and Hamiltonian graphs, trees, matchings, networks, paths and cycles, graph colorings, and planar graphs. Famous problems in Graph Theory include: Minimum Connector Problem (building roads at minimum cost), the Marriage Problem (matching men and women into compatible pairs), the Assignment Problem (filling n jobs in the best way), the Network Flow Problem (maximizing flow in a network), the Committee Scheduling Problem (using the fewest time slots), the Four Color Problem (coloring maps with four colors so that adjacent regions have different colors), and the Traveling Salesman Problem (visiting n cities with minimum cost).

Course learning outcomes
1. Interpret graphs both as mathematical objects, data structures, unifying abstraction of natural and computing systems.
2. Discuss a variety of graph properties and their interrelatedness.
3. Apply skills acquired in discrete mathematics, linear algebra and/or computation to study graph properties.
4. Formulate solutions to a problem arising in the real-life, science, or engineering related to graph theory in team setting.

Linear Programming is a subfield of Optimization which concerns itself with analyzing and finding maximal/minimal values of linear functions whose variables are subject to a given system of linear equations and/or inequalities. Linear Programming problems are encountered in many practical applications (e.g., manufacturing, scheduling, transportation) and are used to aid solutions of other harder optimization problems (e.g. Integer Programming). The aim of this course is to introduce theoretical and practical aspects of Linear Programming. In this course, we will learn how to formulate real-life problems into a linear programming problem (or shortly a linear program), understand its geometrical implications/interpretations, study simplex, ellipsoid (if time permits) and interior point methods to solve linear programs, cover duality theory and sensitivity analysis and introduce integer programming, robust optimization (if time permits), semidefinite programming (if time permits) and the concept of LP relaxation.

Course learning outcomes
1. Solve small-dimensional linear and integer programming problems and simple practical optimization tasks without the aid of a computer (PLO 1, Bloom’s taxonomy level 3).
2. Analyze the solutions of a linear program using the fundamental techniques and general theory of Linear Programming (PLO 1, Bloom’s taxonomy level 4).
3. Recommend an effective strategy for solving a given small-dimensional linear program (PLO 1, Bloom’s taxonomy level 5).
4. Make engaging video presentations of mathematical content (PLO 4, Bloom’s taxonomy level 3).
5. Practice giving and receiving feedback to/from peers on performance of mathematical and computational tasks (PLO 6, Bloom’s taxonomy level 3).

This course represents a first introduction to classical number theory, with possible topics such as: the Euclidean algorithm, the Fundamental Theorem of Arithmetic, congruences, diophantine equations, Fermat and Wilson Theorems, quadratic residues, continued fractions, and the prime number theorem.

Course learning outcomes
1. Apply Divisibility and unique factorization in various rings (integers, Gaussian integers).
2. Use discrete techniques in proofs, such as induction and descent.
3. Apply Euclidean Algorithm and Congruences and Modular Arithmetic.
4. Apply Primitive Roots, Multiplicative Functions.
5. Prove Fermat’s, Euler’s and Wilson’s Theorems.
6. Apply Quadratic residues and quadratic reciprocity.

Descriptive statistics, measures of location and spread, graphic methods, basic probability properties, Bayes’ rule, probability distributions, expected value and variance, binomial and normal distributions, point and interval estimation, hypothesis testing, one-sample and two-sample t-tests, chi-square tests, linear regression, quality measures, and assumption verification, ANOVA and multiple comparisons.

Course learning outcomes
1. Use statistical software to summarize numerically, visualize, and analyze data.
2. Apply estimation and testing methods to analyze single variables or the relationship between two variables in order to understand natural phenomena and make data-based decisions.
3. Model numerical response variables using a single explanatory variable or multiple explanatory variables in order to investigate relationships between variables.
4. Interpret results correctly, effectively, and in context without relying on statistical jargon.
5. Critique data-based claims and evaluate data-based decisions.

This course covers the topics for the Financial Mathematics (FM) exam recommended by the Society of Actuaries (SDA). It covers the fundamental concepts of financial mathematics, and some basic methods for calculating present and accumulated values for various lines of cash flows as a basis for use in: reserving, valuation, pricing, asset/liability management, investment income, capital budgeting and valuing contingent cash flows with applications.

Course learning outcomes
1. Formulate a financial transaction in mathematical form using the notions of accumulated value, present value, and equation of value.
2. Apply annuity concepts such as level-payment annuity, increasing /decreasing annuity, and arithmetic/geometric annuity in financial planning models.
3. Set up loan repayment schemes using the amortization and sinking fund methods.
4. Design pricing strategies to estimate the price of bonds (callable, putable, and zero-coupon) using parameters such as face value, coupon rate, redemption amount, and yield rate.
5. Evaluate alternative investment opportunities by estimating the internal rate of return and discounted cash flow methods.

Chemostat model, Predator – Prey system, the Lotka – Volterra equation, multiple species models, infectious disease models, Michaelis – Menten kinetics, sigmoidal kinetics, threshold – governed cellular development, a biomolecular switch, the activator inhibitor switch, the Hodgkin – Huxley equation, Fitzhugh’s analysis, The Poincare – Bendixson theory, cubic nullclines, the Fitzhugh - Nagumo model, the Hopf bifurcation, oscillation in population – based models, oscillation in a chemical system, cell division, insect population, propagation of annual plants, fixed points and linear stability analysis of systems of discrete time equations.

Course learning outcomes
1. Construct mathematical models of evolution.
2. Apply techniques from differential equations to describe spread of disease and other biological material.
3. Find the equilibria of a single-population model and their stability.
4. Apply techniques from nonlinear differential equations to explain the oscillation in population dynamics and chemical systems.

The course is the second course in abstract algebra. This course covers field extensions, group theory through the isomorphism theorems and Sylow theorems.

Course learning outcomes
1. Know the notions of a field extension, algebraic extension and a finite field.
2. Use group actions to study ring properties.
3. Know the notions of Sylow groups and their applications.
4. Know the notions of field automorphisms and splitting fields.
5. Apply the concepts of Galois theory to study field extensions.
6. Know how to work with Eucleadian domains, PIDs and UFDs.
7. Know applications of group theory in topology.

This course covers an introduction into convex sets and convex functions, unconstrained and constrained optimization, existence of solutions (Weierstrass' theorem), unconstrained optimization: first and second order conditions, equality constraints: Lagrange optimality theorem, second order conditions, inequality constraints: Karush-Kuhn-Tucker theorem, convex and non-convex optimization, some computational methods: line search, steepest descent, Newton, quasi Newton, trust region, feasible points, penalty methods, and augmented Lagrangian methods.

Course learning outcomes
1. Apply the concept of convexity and Fenchel-Rockafellar duality.
2. Apply optimization techniques in convex metric spaces.
3. Use Lagrange duality principle.
4. Apply dynamic programming principle.
5. Apply Pontryagin maximum principle.

The course is an introduction to modern cryptographic algorithms and to their cryptanalysis, with an emphasis on the fundamental principles of information security. Topics include: classical cryptosystems, modern block and stream ciphers, public key ciphers, digital signatures, hash functions, key distribution and agreement.

Course learning outcomes
1. Understand classical and modern approaches to encryption.
2. Understand public-key cryptography.
3. Understand the difference between absolute and computational security.
4. Perform some simple cryptanalysis under various assumptions.

This course is an introduction to life insurance mathematics, it covers mathematical aspects of survival models, life annuities, premium setting and valuation of life insurance (with benefits payable at survival or death), and pension benefits.

Course learning outcomes
1. Use simple probability and actuarial notation concepts to model future lifetimes as random variables.
2. Define a life table at different ages to measure mortality, survival patterns of the population, and the life expectancy of a population at varying ages.
3. Set up life insurance contracts (whole life insurance, endowment insurance, and term insurance).
4. Set up and calculate insurance premiums for the insurance policy when the insured life is subject to some extra level of risk.

The course aims to cover knowledge of basic financial actuarial models with applications and to prepare students pass the actuarial financial economics (MFE) exam. Basic knowledge of calculus, probability, and interest theory are assumed. The course will develop an understanding of: - option pricing models - option hedging techniques - interest rate models - the Black-Scholes model

Course learning outcomes
1. Employ the theory of arbitrage.
2. Understand derivative pricing.
3. Apply Binomial models.
4. Use Ito Lemma ( Black-Scholes PDE).

First part of this course deals with the discrete-time Markov Chains. More specifically, we cover the Markov property, transition matrix, transition probabilities, Chapman-Kolmogorov equation, classification states, and long-time behavior of Markov chains. Second part of this course deals with the continuous-time Markov chains. To be more specific, we cover exponential random variables and lack of memory property, Poisson processes, and more generally, the continuous-time Markov chain and some applications. We introduce the forward/ backward equations of a continuous-time Markov chain and Brownian Motion.

Course learning outcomes
1. Understand the concept of random walks.
2. Calculate conditional expectation.
3. Apply Markov chains in probabilistic models.
4. Use Poisson processes in probabilistic models.
5. Formulate a real-life situation mathematically.

Stochastic Calculus treats “stochastic” integration and “stochastic” differential equations. This subject is usually a graduate course, which requires graduate real analysis and graduate probability as prerequisites, but this course introduces elementary concepts at “NU undergraduate students’ level”. Stochastic Calculus is an essential tool for finance (e.g. pricing options). This course introduces the basic concepts of Stochastic processes, Brownian motion, Martingales, Stochastic (Ito) integration, Stochastic differential equations and the famous Black-Scholes option pricing formula.

Course learning outcomes
1. Apply measure theoretic probability concepts.
2. Understand the basic concepts (properties) of Stochastic processes, Brownian motion and Martingales.
3. Understand the basic concepts stochastic integration, i.e., Ito integral and Ito Lemma.
4. Understand the basic concepts of stochastic differential equations and solve them by using the Ito Lemma.
5. Understand Black-Scholes option pricing formula.

The course material consists of a review and expansion of some topics of calculus of several variables; especially the inverse and implicit function theorems, which are essential tools. Then the classical matrix groups and their properties will be studied, along with their Lie algebras. Finally, representations of SO(3) and SL(n, C) will be studied, among others.

Course learning outcomes
1. Describe the classical matrix Lie groups.
2. Introduce the matrix exponential.
3. Describe the classical matrix Lie algebras.
4. Define abstract Lie algebras.
5. Define and construct basic examples of representations, such as the adjoint representation, dual representation.
6. Recognize irreducible representations.
7. Do computations with representations of basic groups such as SO(3).

This course treats integration theory. First, we review Riemann integration, and then learn Riemann Stieltjes integral. For the rest of the course, we treat Lebesgue measure, Lebesgue integration on Rn, and Lp space. If time permits, we introduce general measure theory and its connection to probability theory.

Course learning outcomes
1. Be able to understand and state definitions of Riemann integral, functions of bounded variation, Riemann-Stieltjes integral, Lebesgue outer measure, Lebesgue measure, and Lebesgue integral.
2. Be able to understand various theorems for Riemann-, Riemann-Stieltjes-, and Lebesgue integrability, and the ideas in their proofs.
3. Be able to state theorems for interchange of limiting operation and integral, and various theorems for Lp space, and to understand the ideas in their proofs.

This course treats integration theory. First, we review Riemann integration, and then learn Riemann Stieltjes integral. For the rest of the course, we treat Lebesgue measure, Lebesgue integration on Rn, and Lp space. If time permits, we introduce general measure theory and its connection to probability theory.

Course learning outcomes
1. Be able to understand and state definitions of Riemann integral, functions of bounded variation, Riemann-Stieltjes integral, Lebesgue outer measure, Lebesgue measure, and Lebesgue integral.
2. Be able to understand various theorems for Riemann-, Riemann-Stieltjes-, and Lebesgue integrability, and the ideas in their proofs.
3. Be able to state theorems for interchange of limiting operation and integral, and various theorems for Lp space, and to understand the ideas in their proofs.

This course is designed to introduce some advanced topics not covered in MATH 273 and study further some concepts covered in MATH 273. This course is a theorem-proofs style course, emphasizing theories. We will cover vector spaces; quotients; dual space; determinants; traces; eigenvalues, eigenvectors and diagonalization; inner product spaces and the spectral theorem for normal operators; singular value decomposition; and, Jordan canonical form.

Course learning outcomes
1. Define Quotients of Vector Space.
2. Define the dual space and the dual map.
3. Understand the spectral theorem and its proof.
4. Understand the singular value decomposition and perform it.
5. Understand the Cayley-Hamilton Theorem and its proof.

The course studies nonlinear differential equations and the time-behavior of their solutions. The course begins with a quick review on first order (logistic) differential equations, and continues with classification into (non) autonomous and (non) linear equations, interpretation of the solution and its general and near equilibrium behavior, the phase-plane, Poincare map, critical points, periodic solutions, Poincare-Bendixson theorem, the concept of stability (Lyapunov), stability analysis by linearization, perturbation theory, Poincare-Lindstedt method, averaging, bifurcation, one dimensional chaos, fractal sets, and Hamiltonian systems.

Course learning outcomes
1. Sketch and interpret phase diagrams.
2. Distinguish between stable and unstable equilibrium points.
3. Use linear approximation methods for analyzing dynamical systems.
4. Find limit cycles and describe their stability.
5. Understand and apply the concepts of Lyapunov stability.

The course is a blend of conceptual and practical aspects of numerical solutions of partial differential equations, and aims at students of senior level. Various numerical methods are discussed: finite difference, finite volume, finite element, and spectral methods, and explicit/implicit methods for time integration. Conceptual aspects include convergence, consistency, stability, Courant-Friedrichs-Lewy criteria, Lax equivalence theorem, error analysis, Fourier-von Neumann stability analysis. Discussions are tailored towards numerical solutins of model problems: Poisson equation, heat equation, advection equation, wave equation, advection-diffusion equation, and Stokes equation. Students are required to implement some methods in Matlab for 1D/2D Poisson, advection, and advection-diffusion equations.

Course learning outcomes
1. Apply numerical methods for solving boundary value problems for parabolic, hyperbolic and elliptic partial differential equations.
2. Use several discretization procedures for reducing a boundary value problem into a algebraic system and solve the equations numerically.
3. Apply spatial discretization methods and time integrators for reducing an initial boundary value problem into a system of differential equations and solve them numerically.
4. Discuss applications of the boundary value and initial/boundary value problems in science and engineering.
5. Be able to develop and implement some numerical procedures for solutions of a project problem approved by the instructor.

This will be first look at complex analysis. In the introduction, properties of complex numbers, limits and topology in the complex plane will be covered. Then the properties of analytic functions will be studied, ending in a proof of Cauchy's theorem. Power series, Laurent series and residues will finish the core part of the course. Applications of contour integration will be covered. As time permits, the instructor may cover basic conformal mappings. Prerequisite: MATH 263 Calculus III.

Course learning outcomes
1. Compute the complex exponential, logarithm, and root functions and know their domains of definition, find the harmonic conjugate to a harmonic function.
2. Interpret analytic functions in terms of power series and Laurent series.
3. Calculate complex line integrals and some improper real integrals using Cauchy’s integral theorem.
4. Solve problems of finding the number of zeroes and poles within a given curve using the argument principle or Rouche’s theorem.

This course is an introductory course on partial differential equations. It focuses on classical linear and quasi-linear partial differential equations. It begins with the classification of partial differential equations (hyperbolic, parabolic, and elliptic) and derivations of some model problems (heat, wave, and Laplace equation). Solution methods for model problems are discussed and also the existence and uniqueness of solutions. At the end some equations from Physics and nonlinear problems will be considered.

Course learning outcomes
1. Solve first- and second-order linear equations using the method of characteristics and some first order nonlinear equations.
2. Classify second order linear equations.
3. Solve the initial value problem for the heat and wave equations on the whole/half line.
4. Compute solutions of inhomogeneous partial differential equations.
5. Examine uniqueness of solutions using energy methods or the maximum principle.
6. Identify basic properties of equations of mathematical physics.

This course introduces the topics of Fourier series and Fourier transform, with applications to differential equations and orthogonal polynomials.

Course learning outcomes
1. Expand functions into Fourier series, investigate convergence of Fourier series, apply Fourier series to solve problems from physics and engineering.
2. Understand the concept of orthogonal sets of functions; the concept of inner product of functions; the concept of L2 spaces: basic facts about Lebesgue integration, L2-convergence and completeness; understand the geometry of Fourier series; apply the above concepts to solve some basic boundary value problems.
3. Perform Fourier transforms; understand the basic properties of Fourier transform; apply Fourier transform to solve ordinary and partial differential equations.
4. Understand the difference between continuous and discrete Wavelet transform; construct orthonormal wavelets.

The course explores the use of multivariate methodology in statistics and its applications. The main focus is placed on multivariate normal distribution, canonical correlation, discriminant analysis, cluster analysis, and principal components. Other topics may be covered as time allows.

Course learning outcomes
1. Use common visualization displays for presenting multivariate data.
2. Utilize the properties of the multivariate normal distribution to investigate the correlation and dependency structure among components.
3. Use the characterizations of the multivariate normal distribution in assessing the normality of data.
4. Apply the multivariate normal distribution to dimensionality reduction techniques, such as canonical correlation analysis and finding principal components.
5. Utilize multivariate models in cluster analysis and classification.

In this course selected topics in advanced mathematics in a particular direction that are not offered as a regular existing course. The aim is to test the response of the students to the particular subject matter and fine tuning the contents before proposing them as a regular course.

Course learning outcomes
1. Prove basic propositions about measures and measure spaces.
2. Prove basic propositions about integrals with respect to a measure.
3. Prove basic propositions involving probabilities.

Under the supervision of a faculty advisor, a student pursues independent research on a topic in, or related to, Mathematics.

Course learning outcomes
1. Perform the study of The Regression: Models, Methods and Applications.
2. Derive properties of Regression models and their extensions.
3. Applications of selected regression models for solving real-world problems.

Under the supervision of a faculty advisor, a student pursues independent research on a topic in, or related to, Mathematics.

Course learning outcomes
1. Perform the study of The Regression: Models, Methods and Applications.
2. Derive properties of Regression models and their extensions.
3. Applications of selected regression models for solving real-world problems.