Mathematics Doctoral

Mathematics

Mathematics (Master's and Doctoral Degrees)

Program Description

The Graduate Program in Mathematics, PPG / MAT, is a consolidated program that stands out for the scientific output of its faculty and the high level of the program. Historical data show that in 1965 postgraduate activities were consolidated with the award of 6 Master's degrees. However, the political crisis that set in at UnB since 1964 culminated in the mass layoff of teachers in 1965, affecting the activities of the Department. From 1971 the Department of Mathematics held a successful process of rebuilding its teaching staff, with the absorption of several doctors trained abroad, thus resuming the academic programs started in 1962.Since its reformulation, the PPG / MAT has graduated 371 masters and 118 doctors.

Aiming to contribute to the formation of human resources and the expansion of knowledge in Mathematics, the permanent faculty maintains an active research program, regularly and actively participates prominently in national and international scientific meetings and in editorial boards of scientific journals. In addition, the faculty maintains scientific exchange activities with institutions at home and abroad (Germany, Argentina, Belgium, Canada, China, Spain, United States, France, England, Italy, Poland, Switzerland , Russia, Turkey and Ukraine) .The postgraduate seminars in the various subareas have an active program of guest researchers and lecturers.

Research Topics

NONCOMMUTATIVE ALGEBRA
GROUP-ASSOCIATED LIE ALGEBRAS
NONLINEAR ANALYSIS, DIFFERENTIAL EQUATIONS
ASYMPTOTIC BEHAVIOR OF NONLINEAR SYSTEMS
DYNAMICS OF FLUIDS.
APPLIED ORDINARY DIFFERENTIAL EQUATIONS
TOOLS FOR ANALYSIS OF NOMINAL RECORD SYSTEMS
MATHEMATICAL PHYSICS
AUTOMORPHIC FORMS AND HYPERBOLIC SURFACES
GEOMETRY OF SUBVARIETIES
RIEMANNIAN GEOMETRY
BURNSIDE GROUPS / REGULAR TREE AUTOMORPHISMS
FINITE GROUPS AND GENERALIZATIONS
PROFINITE GROUPS
IDENTITIES IN GROUPS AND ALGEBRAS
INFERENCE IN STOCHASTIC PROCESSES / ALGORITHMS
LOGIC AND SEMANTICS OF COMPUTING
MATHEMATIC AND COMPUTER MODELING
FINITE GROUP REPRESENTATIONS
SYMMETRIES OF LIE AND ALGEBRIC COMPUTING
ORDINARY EQUATION SYSTEMS WITH SYMMETRIES
CONSERVATION LAW SYSTEMS
INCOMPLETE CHARACTER SUMS
NUMBER THEORY

Courses

The Master student must complete 32 credits from the following courses:

Course	Credits	Code
Algebra 3	5	313149
Linear Algebra 2	5	313165
Analysis 3	5	313246
Analysis of Algorithm and Data Structure	5	313467
Fourier Analysis	5	313173
Functional Analysis	5	313751
Nonlinear Functional Analysis	5	313041
Harmonious Analysis 1	5	313581
Harmonious Analysis 2	5	313424
Numerical Analysis 2	5	313513
Rings and Modules	5	315800
Variation Calculus	5	313181
Cohomology of Groups	5	313017
Ordinary Differential Equations 2	5	313408
Integral Equations	5	313203
Internship in Higher Education Teaching in Mathematics 1	4	318094
Research Internship in Algebra	1	318141
Research Internship and Analysis	1	318175
Research Internship in Differential Geometry	1	318183
Research Internship in Applied Mathematics	1	318191
Mathematical Formalisms in Computing	4	313432
Fundamentals of Mathematics 2	5	313823
Geometry of Differential Forms	5	317934
Differential Geometry	5	313343
Finite Geometry	5	313955
Riemannian Geometry	5	313033
Algebraic Groups	5	313211
Lie Groups	5	313912
Permutation Groups	5	318084
Introduction to Algebra	6	313114
Introduction to Analysis	6	313491
Mathematical Formalisms in Computing	5	313432
Introduction to Probability and Applications	5	313157
Introduction to Number Theory	5	318078
Introduction to Topology	5	313254
Formal and Automaton Languages 2	5	313483
Algebraic Logic	3	313785
Mathematical Methods for Physics 2	5	313530
Algebraic Numbers	5	313891
Combinatorial Optimization and Algorithms	5	313807
Teaching Practice in Mathematics	4	318027
Probability and Theory of Measurement	5	318167
Stochastic Processes 1	5	318086
Dynamic Programming	5	313378
Mathematical Programming	5	343441
Representation of Groups 2	5	313068
Seminar of Algebra	1	313840
Seminar of Linear Functional Analysis	1	313866
Seminar of Non-Linear Functional Analysis	1	313831
Number Analysis Seminar	1	313953
Seminar of Computing	1	313599
Seminar of Partial Differential Equations	1	313301
Seminar of Elliptic Functions	1	313769
Seminar of Fundamentals of Mathematics	1	313971
Seminar of Differential Geometry	1	313874
Seminar of Finite Geometry and Finite Groups	1	313904
Seminar of Logic	1	313777
Seminar of Applied Mathematics	1	313696
Seminar of Mechanics	1	313947
Seminar of Optimization	1	313858
Seminar of Probability	1	313882
DIFFERENTIAL APPLIED SINGULARITY SEMINAR	1	313360
Seminar of Dynamical Systems	1	318302
Seminar in Automorphic Forms and Number Theory	1	318060
Variational Methods	5	313092
Bodies Theory	5	313726
Theory of Finite Groups 1	5	313131
Theory of Finite Groups 2	5	313386
Theory of Models	5	313106
Semigroups and Applications Theory	5	313190
Advances Topics of Differential Geometry	5	318043
Advanced Topics in Mathematics	5	310221
Topics of Numerical Analysis	5	313742
Topics of Linear Programming	5	313335
Introduction to Computing Methods in PDE	5	313611
Topics in Number Theory	5	318051
Topics in Algebra	5	313734
Topics in Mathematic Combination	5	313416
Topics in Mathematic Statistics	5	313921
Introduction to Computing Methods in ODE	5	313637
Advanced Topics in Mathematics	2	310221
Topics in Probability	5	318019
Differential Topology	5	313815
General Topology	5	313238
Complex Varieties	5	318001
Distinguishable Variety	5	313351

The Doctoral candidate must take 48 credits from the following courses:

Course	Credits	Code
Algebra 3	5	313149
Algebra 4	3	313980
Commutative Algebra	5	314544
Linear Algebra 2	5	313165
Lie Algebras	5	313572
Analysis 3	5	313246
Analysis of Algorithm and Data Structure	5	313467
Fourier Analysis	5	313173
Functional Analysis	5	313751
Nonlinear Functional Analysis	5	313041
Harmonious Analysis 1	5	313581
Harmonious Analysis 2	5	313424
Numerical Analysis 2	5	313513
Rings and Modules	5	315800
Presentation of Computational Methods and Groups	5	313629
Variation Calculus	5	313181
Cohomology of Groups	5	313017
Computing Complexity and Computability	5	313475
Ordinary Differential Equations 2	5	313408
Applied Ordinary Differential Equations	5	313548
Partial Differential Equations 1	5	313556
Partial Differential Equations 2	5	313564
Stochastic Differential Equations	5	317942
Integral Equations	5	313203
Internship in Higher Education Teaching in Mathematics 2	4	318108
Research Internship in Algebra	1	318141
Research Internship and Analysis	1	318175
Research Internship in Differential Geometry	1	318183
Research Internship in Applied Mathematics	1	318191
Differential Forms and Applications	5	313319
Fundamentals of Mathematics 2	5	313823
Geometry of Differential Forms	5	317934
Finite Geometry	5	313955
Riemannian Geometry	5	313033
Algebraic Groups	5	313211
Lie Groups	5	313912
Permutation Groups	5	318084
Profinite Groups	5	318124
Classical Logic and Extensions	5	313998
Introduction to Topology	5	313254
Introduction to Differential Equations	5	318159
Formal and Automaton Languages 2	5	313483
Algebraic Logic	3	313785
Analytical Mechanics	5	313122
Measure and Integration	5	313220
Mathematical Methods for Physics 2	5	313530
Algebraic Numbers	5	313891
Combinatorial Optimization and Algorithms	5	313807
Probability and Theory of Measurement	5	318167
Stochastic Processes 1	5	318086
Dynamic Programming	5	313378
Mathematical Programming	5	343441
Representation of Groups 1	5	313050
Representation of Groups 2	5	313068
Seminar of Algebra	1	313840
Seminar of Linear Functional Analysis	1	313866
Seminar of Non-Linear Functional Analysis	1	313831
Number Analysis Seminar	1	313953
Seminar of Computing	1	313599
Seminar of Partial Differential Equations	1	313301
Seminar of Mathematic Physics	5	313505
Seminar in Automorphic Forms and Number Theory	1	318060
Seminar of Elliptic Functions	1	313769
Seminar of Fundamentals of Mathematics	1	313971
Seminar of Differential Geometry	1	313874
Seminar of Finite Geometry and Finite Groups	1	313904
Seminar of Logic	1	313777
Seminar of Applied Mathematics	1	313696
Seminar of Mechanics	1	313947
Seminar of Optimization	1	313858
Seminar of Probability	1	313882
DIFFERENTIAL APPLIED SINGULARITY SEMINAR	1	313360
Seminar of Dynamical Systems	1	318302
Seminar in Automorphic Forms and Number Theory	1	318060
Theory of Automorphic Forms	5	313602
Theory of Probabilities 1	5	313718
Variational Methods	5	313092
Bodies Theory	5	313726
Theory of Finite Groups 2	5	313386
Theory of Models	5	313106
Semigroups and Applications Theory	5	313190
Analysis Advanced Topics	5	313025
Topics in Number Theory	5	318051
Advances Topics of Differential Geometry	5	318043
Advanced Topics in Mathematics	5	310221
Topics of Numerical Analysis	5	313742
Topics in Ordinary Differential Equations	5	318035
Topics of Mathematic Physics	5	313521
Topics of Stochastic Processes	5	318116
Topics of Linear Programming	5	313335
Introduction to Computing Methods in PDE	5	313611
Topics in Number Theory	5	318051
Topics in Algebra	5	313734
Topics in Applied Algebra	5	314536
Topics in Mathematic Combination	5	313416
Topics in Computing	5	318132
Topics in Mathematic Statistics	5	313921
Introduction to Computing Methods in ODE	5	313637
Advanced Topics in Mathematics	2	310221
Topics in Probability	5	318019
Algebraic Topology	5	313394
Differential Topology	5	313815
Complex Variables 2	5	313076
Complex Varieties	5	318001
Distinguishable Variety	5	313351