Mathematics at NEWUU

Undergraduate Program in Applied Mathematics

Graduates of a four-year B.Sc. program in Applied Mathematics, with a strong emphasis on pure mathematics and some computer science, can pursue a wide range of career opportunities in fields that value analytical thinking, problem-solving, and mathematical rigor. These include:

Academic Research and Education
Software Development and Data Science
Cryptography and Cybersecurity
Operations Research and Optimization
Quantitative Finance
Government and Policymaking
Mathematical Consulting

This strong foundation in theoretical mathematics ensures that graduates are well prepared for both academic pursuits and roles in cutting-edge technical fields.

Curriculum – Detailed Study Plan

The Applied Mathematics program at NewUU comprises a total of 244 ECTS credits over four years. This structure ensures a rigorous foundation in theoretical mathematics followed by specialized computational and applied modules.

Lec–Tut/Lab gives the weekly contact hours: lecture, tutorial and, where a course has one, laboratory.

Course titles shown in colour can be opened for a description, the textbook in use and the topics covered.

Year 1: Foundations of Mathematical Sciences

Code	Course Title	Lec–Tut/Lab	ECTS
Semester 1
MATH111	Prerequisite: MATH101	3–2	6
About this course The first course in a sequence of three. It deals with limits, continuity, differentiation and integration, applications of the derivative to determine the shape of graphs, evaluation of limits by l’Hôpital’s rule, finding maximum and minimum values of functions, and problems of finding rates. The course ends with indefinite and definite integrals, integration by parts, u-substitution, trigonometric substitution, integration of rational functions, improper integrals and applications to area problems. Textbook James Stewart et al., Calculus, Metric Version, 9th edition, Cengage Learning Further reading George F. Simmons, Calculus with Analytic Geometry, 2nd edition, McGraw-Hill, 1996 Ernst Hairer, Gerhard Wanner, Analysis by Its History, Springer, 2008 Topics covered The limit of a function, calculating limits Continuity, limits at infinity, horizontal asymptotes Derivatives and rates of change, differentiation formulas, derivatives of trigonometric functions The chain rule, implicit differentiation, inverse functions Derivatives of exponential and logarithmic functions, logarithmic differentiation, hyperbolic functions Curve sketching, maximum and minimum values, the mean value theorem Indeterminate forms and l’Hôpital’s rule Antiderivatives and the definite integral The fundamental theorem of calculus, the substitution rule Applications: areas, volumes, work, average value of a function Integration by parts, trigonometric integrals and substitution Integration of rational functions, improper integrals Arc length, area of a surface of revolution
MATH221		2–2	6
About this course This course provides a background in discrete mathematics as a foundation for further study in computer science, and is also of interest to students wishing to pursue further study in mathematics. Students study propositional and predicate logic, methods of proof, fundamental structures such as sets, functions, relations and equivalence relations, Boolean algebra and digital logic, graphs and trees, and elementary counting techniques. Textbook Kenneth H. Rosen, Discrete Mathematics and Its Applications, 8th edition, McGraw Hill, 2019 Further reading Susanna S. Epp, Discrete Mathematics with Applications, 5th edition, Cengage Learning, 2020 Topics covered Propositional logic: propositions, logical operations, truth tables Propositional equivalences, disjunctive normal form, predicates and quantifiers Nested quantifiers, rules of negation Proof methods and basic structures: sets, functions, sequences, Boolean matrices Growth of functions: big O, Theta, Omega Mathematical induction and strong induction Recursive definitions and structural induction Basics of counting, the pigeonhole principle, permutations and combinations Recurrence relations and divide-and-conquer algorithms Relations, equivalence relations, partial orderings Graph terminology, representation, isomorphism and connectivity Euler and Hamiltonian paths, planar graphs
CS102	Computer Programming 1	2–4	8
HASS101	Academic and Communication Skills 1	0–3	6
HASS100	First Principles of NewUU	3–0	6
Semester 2
MATH211	Prerequisite: MATH111	3–2	6
About this course The second course in a sequence of three. It deals with numerical sequences and series, parametric equations and polar coordinates, scalar functions of several variables and double integrals, with special focus on tests for convergence and divergence of series, and on optimization. Textbook James Stewart et al., Calculus, Metric Version, 9th edition, Cengage Learning Further reading Edwin “Jed” Herman, Gilbert Strang, Calculus, Volumes 1 and 2, 2016 Topics covered Sequences and series The integral test and estimates of sums The comparison tests, alternating series and absolute convergence, the ratio and root tests Strategy for testing series, power series, representation of functions as power series Taylor and Maclaurin series, applications of Taylor polynomials Functions of several variables, limits and continuity Partial derivatives Tangent planes and linear approximations, the chain rule, directional derivatives and the gradient vector Maximum and minimum values Curves defined by parametric equations, calculus with parametric curves Polar coordinates and calculus in polar coordinates Double integrals over rectangles and over general regions Double integrals in polar coordinates, applications to surface areas
MATH201	Prerequisite: MATH101	2–2	6
About this course An introduction to fundamental concepts in linear algebra, including solving linear systems using Gauss-Jordan elimination and other methods, matrix operations and linear transformations. Students explore inverse matrices, image and kernel, basis and dimension, and coordinate representations in vector spaces. The course covers orthonormal bases, the Gram-Schmidt process, QR factorization, determinants, eigenvalues, eigenvectors and matrix diagonalization, with applications to dynamical systems including complex eigenvalues. Textbook Bahodir Ahmedov, Applied Linear Algebra for Engineers: a Lecture-Based Course with Examples, Exercises, and Applications, 1st edition, New Uzbekistan University, 2026 Further reading Howard Anton, Robert C. Busby, Contemporary Linear Algebra Topics covered Geometric and algebraic vectors Vector equations Systems of linear equations Operations with matrices Invertible matrices Matrices in special forms Vector spaces and subspaces Basis and dimension Orthogonality and applications Determinants Eigenvalues and eigenvectors Eigenvalues of symmetric matrices
CS210	Computer Programming 2 Prerequisite: CS102	2–4	8
DSG101	Creative Thinking and Design	3–0	6
HASS111	Academic and Communication Skills 2 Prerequisite: HASS101	0–3	6
Year 1 total			64

Year 2: Abstract Structures and Physical Systems

Code	Course Title	Lec–Tut/Lab	ECTS
Semester 3
MATH222	Prerequisite: MATH211	2–2	6
About this course The third and final part of a three-part calculus sequence. The first half of the course covers multivariable integration, including double and triple integrals and coordinate transformations, as well as vector calculus, including line integrals, surface integrals and the fundamental theorems of vector calculus. The second half introduces Fourier analysis, with emphasis on Fourier series, the Fourier transform, and applications to boundary-value problems such as the vibrating string and the heat equation. Textbook James Stewart, Daniel K. Clegg, Saleem Watson, Calculus, Metric Edition, 9th edition, Cengage Learning, 2020 Elias M. Stein, Rami Shakarchi, Fourier Analysis, Princeton Lectures in Analysis, vol. 1, Princeton University Press, 2003 Further reading Loring W. Tu, An Introduction to Manifolds, 3rd edition, Universitext, Springer, 2026 Walter Rudin, Real and Complex Analysis, 3rd edition, McGraw-Hill, 1987 Topics covered Double and triple integrals Cylindrical and spherical coordinates, change of variables Vector fields, line integrals, the fundamental theorem for line integrals Curl and divergence, Green’s theorem Parametric surfaces and surface integrals The theorems of Gauss and Stokes Motivating Fourier analysis: the wave and heat equations Basic properties of Fourier series, convolutions Convergence and uniqueness of Fourier series The Fourier transform for one real variable and its applications The discrete Fourier transform
MATH202	Prerequisite: MATH201	2–2	6
About this course This course explores advanced topics in linear algebra with a rigorous, proof-based approach. Students develop a deep understanding of vector spaces over R and C, including subspaces, spanning sets, linear independence, bases and dimension. The course covers linear transformations, their kernels and images, invertibility and isomorphisms. Further topics include products and quotients of vector spaces, dual spaces and polynomial representations. The study of invariant subspaces, eigenvalues, eigenvectors and diagonalization gives insight into the structure of linear operators, and inner product spaces lay the foundation for advanced applications. Textbook Kenneth Hoffman, Ray Kunze, Linear Algebra, 2nd edition Further reading David S. Dummit, Richard M. Foote, Abstract Algebra Topics covered Linear equations and matrices Vector spaces Eigenvalues and the Jordan form Inner product spaces
MATH232	Prerequisite: MATH111	2–2	6
About this course A comprehensive course introducing the fundamental concepts and analytical methods of probability and statistics with a focus on real-world applications. Through theoretical lectures, tutorial sessions and computer-based exercises using Python, students explore descriptive statistics, probability theory, discrete and continuous distributions, hypothesis testing, regression analysis and nonparametric methods. The course is designed to develop analytical thinking, problem-solving skills and proficiency in statistical software. Textbook Jung Jin Lee, Introductory Statistics and Data Science using eStat, 2023 Hogg, Tanis, Zimmerman, Probability and Statistical Inference, 9th edition, Pearson, 2015 Further reading John Verzani, simpleR: Using R for Introductory Statistics Topics covered Visualization of qualitative and quantitative data Probability Discrete distributions Continuous distributions Bivariate distributions Distributions of functions of random variables The central limit theorem Point and interval estimation Testing hypotheses for a single population Testing hypotheses for two and for several populations Correlation Simple and multiple linear regression analysis
PHYS101	Physics 1	2–2–2	8
CS111	Algorithms & Data Structures Prerequisite: CS102	2–2	6
Semester 4
MATH250	Prerequisite: MATH211	2–2	6
About this course An introduction to the fundamental concepts of topology, including metric spaces, topological spaces, continuity, compactness, connectedness and fundamental groups. Applications to analysis and algebraic topology are discussed. Textbook James R. Munkres, Topology, 2nd edition, Prentice Hall, 2000 Allen Hatcher, Algebraic Topology, 2002 (freely available online) Further reading J. P. May, A Concise Course in Algebraic Topology James R. Munkres, Elements of Algebraic Topology William S. Massey, A Basic Course in Algebraic Topology Topics covered Metric spaces: metrics, open balls, the induced topology on Rⁿ Topological spaces, bases, continuity, homeomorphisms, closure, interior, boundary Subspace and product topologies Quotient spaces and identifications Connectedness, path-connectedness, components Compactness, the Heine-Borel theorem Separation axioms: T₁ and Hausdorff spaces Homotopy, homotopy equivalence, deformation retracts, contractibility The fundamental group: definition, basepoints, functoriality, first computations The van Kampen theorem and its computations Covering spaces, path lifting and homotopy lifting Singular homology: chain complexes, the boundary operator, homotopy invariance Homology of spheres and of the torus The relation between the fundamental group and first homology
MATH270	Prerequisite: MATH201, MATH221	2–2	6
About this course An introduction to algebraic structures including groups, rings and fields, with emphasis on theory and proof-writing skills. Textbook Malik, Mordeson, Sen, Fundamentals of Abstract Algebra, WCB McGraw-Hill, 1997 Further reading Joseph A. Gallian, Contemporary Abstract Algebra, 8th edition, Cengage Learning, 2012 Topics covered Sets and equivalence relations Magmas, binary operations, monoids Groups and examples Permutations Subgroups, normal subgroups, quotients Homomorphisms and direct sums Rings and examples Subrings and ideals Polynomial rings Prime and maximal ideals Fields and field extensions Finite fields
MATH241	Prerequisite: MATH211, MATH201	3–1	6
About this course An introduction to ordinary differential equations, covering methods for solving first-order and higher-order equations, including linear, separable and exact equations. Students explore solutions with constant and variable coefficients, power series methods and Laplace transforms. The course also introduces systems of linear differential equations, using matrix methods and phase portraits, and studies nonlinear systems with a focus on stability and linearization. Emphasis is placed on both analytical and numerical techniques. Textbook Dennis G. Zill, A First Course in Differential Equations with Modeling Applications, 11th edition, Brooks/Cole, Cengage Learning Further reading George F. Simmons, Differential Equations with Applications and Historical Notes, CRC Press Topics covered First-order differential equations Higher-order differential equations Series solutions of linear equations The Laplace transform Systems of linear first-order differential equations Qualitative properties of solutions, the Sturm comparison theorem
HASS110	History of Uzbekistan	2–0	4
PHYS111	Physics 2 Prerequisite: PHYS101	2–2–2	8
Year 2 total			62

Year 3: Computational Modeling and Optimization

Code	Course Title	Lec–Tut/Lab	ECTS
Semester 5
MATH311	Prerequisite: MATH241	2–2	6
About this course An introduction to the theory and methods of solving partial differential equations, with applications to physics and engineering. Topics include first-order PDEs, classification of second-order PDEs, separation of variables, Fourier series and transforms, Green’s functions and numerical methods. Textbook Stanley J. Farlow, Partial Differential Equations for Scientists and Engineers Walter A. Strauss, Partial Differential Equations: An Introduction, 2nd edition Further reading Russell Herman, Introduction to Partial Differential Equations Richard Haberman, Applied Partial Differential Equations Topics covered PDEs versus ODEs, classification into elliptic, parabolic and hyperbolic Examples from physics: the heat, wave and Laplace equations Boundary conditions: Dirichlet, Neumann, Robin Linear and quasi-linear first-order PDEs, the method of characteristics The Laplace equation, harmonic functions and the mean value theorem The heat equation, separation of variables, Fourier series solutions The wave equation, d’Alembert’s solution, standing waves Orthogonal functions, Fourier expansions, Sturm-Liouville theory Heat and wave equations in two and three dimensions Laplace’s equation in polar, cylindrical and spherical coordinates Finite difference methods, stability and convergence analysis Case studies in fluid dynamics and quantum mechanics
MATH303	Prerequisite: MATH211	2–2	6
About this course A comprehensive course introducing the fundamental concepts and analytical methods of game theory with a focus on real-world applications across economics, business and engineering. Through lectures and tutorial sessions, students explore normal form games, Nash equilibria, extensive form games, Bayesian games, cooperative games, Stackelberg games and learning in games. The course develops analytical thinking and problem-solving skills, preparing students to apply game-theoretic models to real scenarios, understand different solution concepts, and recognize the importance of information and its impact on decision making. Textbook Martin J. Osborne, Ariel Rubinstein, A Course in Game Theory, MIT Press Further reading Martin J. Osborne, An Introduction to Game Theory, Oxford University Press Topics covered Preferences, payoffs and strategic games, best responses and Nash equilibrium Pure equilibria, dominance and iterated elimination Expected utility and mixed strategies Existence of mixed equilibrium, zero-sum games and minimax Correlated equilibrium and rationalizability Extensive games, backward induction, subgame-perfect equilibrium Bargaining, alternating offers and discounting Finitely and infinitely repeated games, sustaining cooperation Bayesian games: types, beliefs and Bayesian Nash equilibrium Sequential rationality, signalling and sequential equilibrium Coalitional games, the core and the Shapley value Syllabus not yet approved
MATH321		2–2	6
About this course This course introduces elementary number theory and its role in modern cryptography. Number theory studies the additive and multiplicative structures of the integers and the solutions of equations involving them, while cryptography provides methods for secure communication. The course develops divisibility, congruences and the arithmetic of the integers modulo n, and explores the number-theoretic structures and algorithms central to cryptographic applications. These ideas motivate and analyze classical and public-key schemes, illustrating how mathematical assumptions underpin security. Textbook Kenneth H. Rosen, Elementary Number Theory and Its Applications, 6th edition, Pearson Addison Wesley, 2011 Topics covered Private key encryption Arithmetic modulo n Greatest common divisors and the Euclidean algorithm The fundamental theorem of arithmetic Factoring integers The Sun-Jiushao theorem Units modulo n and the group structure of (Z/n)* Primality tests and factorization Public key encryption Quadratic reciprocity
MATH390		2–2	6
About this course This course equips students with the essential skills for writing, formatting and presenting scientific content. It introduces LaTeX for professional document preparation, best practices for structuring research papers, and techniques for delivering clear presentations. Students also develop critical reading and summarization skills by analyzing and summarizing scientific papers as part of a semester project. Textbook Stephen B. Heard, The Scientist’s Guide to Writing, 2nd edition Further reading LearnLaTeX.org (free) Michael Alley, The Craft of Scientific Presentations, selected chapters Topics covered LaTeX basics Figures, tables, equations, citations and BibTeX How to read a scientific paper Abstracts, introductions, organization and scientific style Writing a LaTeX summary and review of a chosen paper Presenting with slides
CS212	Design & Analysis of Algorithms Prerequisite: CS111	2–2	6
Semester 6
MATH233	Prerequisite: MATH211	2–2	6
About this course A rigorous introduction to the mathematical foundations of optimization, including unconstrained and constrained optimization, convex analysis, duality theory and numerical methods. Applications to economics, engineering and machine learning are explored. Textbook Jasbir S. Arora, Introduction to Optimum Design, 4th edition, Elsevier, 2016 Further reading Jorge Nocedal, Stephen J. Wright, Numerical Optimization, 2nd edition, Springer Series in Operations Research and Financial Engineering, Springer, 2006 Topics covered Optimization problem formulation and the general mathematical model Graphical solution, introduction to MATLAB Global and local minima, gradient, Hessian Taylor series, quadratic forms, optimality conditions for unconstrained problems Optimality conditions for constrained problems Linear programming concepts and the standard LP form The simplex method Numerical methods for unconstrained optimization Step size determination methods Linearization of the constrained problem Sequential linear programming
MATH313	Prerequisite: MATH211	2–2	6
About this course A rigorous introduction to numerical methods for solving mathematical problems arising in science and engineering, with a special focus on partial differential equations. Topics include error analysis, numerical solutions of nonlinear equations, interpolation, numerical differentiation and integration, numerical linear algebra, and numerical solutions of ordinary and partial differential equations. The PDE component covers finite difference methods, finite element methods, stability analysis and spectral methods. Learning outcomes Understand sources of numerical errors and their impact on computations Solve nonlinear equations using numerical methods such as bisection and Newton’s method Apply interpolation techniques such as Lagrange and spline interpolation Perform numerical differentiation and integration using Newton-Cotes formulas and Gaussian quadrature Solve systems of linear equations by direct and iterative methods such as LU decomposition and Gauss-Seidel Implement numerical methods for eigenvalue problems and least-squares approximations Apply numerical techniques to ordinary differential equations, including Euler and Runge-Kutta methods Develop and analyze finite difference methods for the heat, wave and Laplace equations Understand stability, consistency and convergence of numerical schemes for PDEs Explore finite element and spectral methods for PDEs in complex geometries
MATH305	Prerequisite: MATH222	2–2	6
About this course An introduction to the theory of complex functions, covering analytic functions, Cauchy’s integral theorem, power series representations, Laurent series, the residue theorem and conformal mappings. Applications to real integrals and potential theory are explored. Textbook Henri Cartan, Elementary Theory of Analytic Functions of One or Several Complex Variables, Dover Publications, 1973 edition Further reading Lars Ahlfors, Complex Analysis, 3rd edition, American Mathematical Society Topics covered Complex numbers, their geometric representation, formal power series Convergence of power series Differentiation of power series, logarithmic and exponential functions Line integrals and complex integration, the Cauchy integral formula Closed and exact differential forms, homotopy Holomorphic functions and Cauchy’s theorem, analytic continuation Further forms of the Cauchy integral formula and their applications Liouville’s theorem, the mean value property, the maximum principle Schwarz’s lemma, Laurent expansion The residue theorem Applications of the residue theorem to real definite integrals Power series and analytic functions in several variables Harmonic functions and conformal mapping Convergence of sequences of holomorphic functions, the Riemann mapping theorem
HASS305	Philosophy	3–0	6
TBD	CS Free Elective	2–2	6
Year 3 total			60

Year 4: Specialization and Thesis

Code	Course Title	Lec–Tut/Lab	ECTS
Semester 7
MATH406	Prerequisite: MATH250, MATH202	2–2	6
About this course This course provides a rigorous foundation in real analysis, measure theory and elements of functional analysis, emphasizing Lebesgue integration, Banach and Hilbert spaces, and applications to Fourier analysis and partial differential equations. Topics include measure and integration theory, L^p spaces, the Radon-Nikodym theorem, the Hahn-Banach and open mapping theorems, spectral theory and weak convergence methods. The course prepares students for advanced topics in analysis and applied mathematics. Textbook Sheldon Axler, Measure, Integration & Real Analysis, Graduate Texts in Mathematics, vol. 282, Springer, 2020 (open-access edition at measure.axler.net) Further reading Haïm Brezis, Functional Analysis, Sobolev Spaces and Partial Differential Equations, Universitext, Springer, 2011 Topics covered Countable and uncountable sets, σ-algebras, measurable spaces Measures and measure spaces, Lebesgue measure on R, null sets Measurable and simple functions, almost-everywhere convergence Construction of the Lebesgue integral, comparison with the Riemann integral The dominated convergence theorem, interchanging limits and integrals Product measure and Fubini’s theorem L^p spaces, the Hölder and Minkowski inequalities Banach spaces, bounded linear functionals, the Hahn-Banach theorem Bounded linear operators, the open mapping theorem, uniform boundedness Hilbert spaces, orthogonality, orthonormal bases, Fourier series Compact operators and the spectral theory of compact self-adjoint operators Weak and weak* convergence, applications to weak formulations of PDEs
MATH402	Prerequisite: MATH221	2–2	6
About this course This course develops the fundamental methods of combinatorial analysis, building on prior knowledge of discrete mathematics and elementary counting. Topics include combinatorial identities, generating functions, recurrence relations, inclusion-exclusion, Stirling numbers, counting under symmetry, Ramsey theory, matchings, network flows and selected topics in graph theory. Emphasis is placed on bijective arguments, double counting, algebraic methods, and the connections between combinatorial theorems and algorithms. Textbook George Pólya, Robert E. Tarjan, Donald R. Woods, Notes on Introductory Combinatorics, Springer-Verlag Further reading László Lovász, József Pelikán, Katalin Vesztergombi, Discrete Mathematics: Elementary and Beyond Topics covered Sum and product rules, permutations and combinations Combinatorial proofs: bijections, Pascal’s identity, double counting Counting with repetitions, multisets, stars and bars Binomial identities, Vandermonde’s identity Generating functions: formal power series, products and convolution Generating-function models, coefficient extraction Recurrences and their solution by generating functions Inclusion-exclusion, derangements, counting onto functions Stirling numbers of the first and second kinds Counting up to symmetry, Burnside’s lemma Cycle indices and Pólya enumeration Ramsey theory, monochromatic configurations, R(3,3) = 6 Stable marriage, bipartite matchings, Hall’s condition Maximum matchings, augmenting paths, network flows, max-flow min-cut Eulerian and Hamiltonian paths and cycles Graph coloring Syllabus not yet approved
TBD	Math Free Elective	2–2	6
TBD	CS Free Elective	2–2	6
GRAD490	Graduation Project 1 / Internship 1	2–0	8
Semester 8
MATH403	Prerequisite: MATH270, MATH250	2–2	6
About this course An introduction to the fundamental concepts of algebraic geometry, focusing on affine and projective varieties, polynomial equations and their geometric interpretations. Students explore coordinate rings, ideals and morphisms between varieties, with an emphasis on examples and computational techniques. The course also covers basic intersection theory, dimension theory, and applications in physics and coding theory. Learning outcomes Understand affine and projective varieties as solution sets of polynomial equations Use the coordinate ring and the Nullstellensatz to study the algebra-geometry correspondence Apply Gröbner bases and computational techniques to solve polynomial systems Analyze morphisms between varieties and their geometric meaning Develop intuition for dimension theory and intersection theory Explore applications of algebraic geometry in physics, cryptography and coding theory Gain familiarity with computational tools such as Macaulay2 and SageMath
MATH414	Prerequisite: MATH232	2–2	6
About this course A rigorous foundation in probability theory and statistical inference, emphasizing measure-theoretic probability, convergence of random variables and asymptotic methods. Topics include probability spaces, laws of large numbers, central limit theorems, stochastic processes, statistical estimation theory, hypothesis testing, Bayesian methods and modern statistical learning approaches. Applications to finance, machine learning and stochastic modelling are explored. Learning outcomes Understand the measure-theoretic foundations of probability, including probability spaces and σ-algebras Prove and apply the key limit theorems: the weak and strong laws of large numbers and the central limit theorem Analyze convergence of random variables in distribution, in probability and almost surely Study stochastic processes such as Markov chains and Brownian motion Apply principles of statistical inference, including maximum likelihood and Bayesian estimation Develop and evaluate hypothesis testing procedures, including Neyman-Pearson theory and likelihood ratio tests Explore asymptotic methods: consistency, efficiency and asymptotic normality of estimators Implement statistical methods in finance, risk modelling and machine learning
HASS200	Communications Ethics	3–0	6
GRAD491	Graduation Project 2 / Internship 2	2–0	8
Year 4 total			58

Total: 244 ECTS credits.

Ph.D. Program

The Department of Mathematics supervises doctoral research in algebra. At present this is the only specialty in which the department admits doctoral students.

01.01.06 Algebra

This is a local Ph.D. (Doctor of Philosophy) programme, run under the national regulations of the Republic of Uzbekistan, and admission is open to citizens of Uzbekistan only. It can be taken either full-time or part-time as an independent researcher. Prospective supervisors and their research interests are listed on the People page.

Admission requirements

A Master’s degree, or an equivalent diploma of higher education, in a relevant specialty.
At least one scientific article published in a scientific journal.
At least two abstracts in the proceedings of scientific conferences in relevant fields, which can serve as a basis for the doctoral dissertation.
An English proficiency certificate at B2 or above. Applicants who completed their bachelor’s or master’s degree in English do not need to provide one.

Documents to submit

Both routes require a statement, a CV, a copy of the master’s diploma or equivalent, a certified copy of the employee record book, a list of published scientific papers with copies, and the English certificate.

Full-time applicants holding the Government Scholarship of the President of the Republic of Uzbekistan must also submit a copy of the relevant document.
Independent researchers must also submit recommendation(s) from their employer, head of department or supervisors.

Dates

Applications, full-time: 5 October – 5 November
Applications, independent researcher: Quarterly: 5 October – 5 November, 15 January – 15 February, 15 April – 15 May, 15 July – 15 August
Entrance examinations: 5 – 25 November, annually
Results announced: By 5 December
Studies begin: January of the following year

How to apply

All applications go through daraja.ilmiy.uz. For questions about the doctoral programmes, write to admission@newuu.uz or call +998 71 202-41-11. For questions about supervision in algebra, write to math@newuu.uz.

New Uzbekistan University offers doctoral study in ten specialties in total. The full list, together with the current admission rules, is on the university’s Ph.D. programmes page, which is the authoritative source if any detail here is out of date.

2+2 Degree and Transfer

Under discussion. The Department of Mathematics is in discussion with The Hong Kong Polytechnic University (PolyU) about a dual degree pathway, under which students would spend their first two years at New Uzbekistan University and their final two years at PolyU, graduating with a degree from each university.

Nothing below is final. The curriculum mapping is still in draft and the arrangement has to be agreed by both universities before any student can be admitted to it. This page will be updated as the discussions progress.

The proposed pathway

For students admitted to the B.Sc. in Applied Mathematics at New Uzbekistan University in the 2025/26 and 2026/27 academic years:

B.Sc. in Applied Mathematics (New Uzbekistan University) with B.Sc. (Hons) in Applied Mathematics (PolyU)

Under the proposal, students would complete two years at New Uzbekistan University and then continue at PolyU: the 2025/26 intake from September 2027, and the 2026/27 intake from September 2028.

Studying abroad in the meantime

Students who want to spend part of their degree abroad can already do so through the university’s exchange agreements. New Uzbekistan University has exchange partnerships with more than fifty universities. These are semester- or year-long exchanges rather than a dual degree, and they are arranged centrally rather than by the department.

Who to ask

For current information about studying abroad, exchange places and the dual degree discussions, contact:

Oxana Budjko: International Relations Department
o.budjko@newuu.uz

The university’s International Office page lists the current partner universities and is the authoritative source if any detail here is out of date.

Undergraduate Program in Applied Mathematics

Curriculum – Detailed Study Plan

Year 1: Foundations of Mathematical Sciences

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Year 2: Abstract Structures and Physical Systems

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Year 3: Computational Modeling and Optimization

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Year 4: Specialization and Thesis

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