Applied Mathematics Field

 | Post date: 2021/06/29 | 

 
Applied mathematics field:
 
The postgraduate course of the Department of Applied Mathematics started in 1995 with the establishment of the master's degree program and in 1996 with the doctoral course.
At present, the Department of Applied Mathematics accepts about 25 Postgraduate students and about 10 doctoral students annually.
The syllabus of the courses of the Department of Applied Mathematics is as follows:
 
Numerical Analysis branch:
Compulsory Courses:
 
NO Course Units
1 Advanced numerical analysis 3
2 Real analysis 3


 
Numerical Analysis branch: Specialized courses – optional: 
No Course Units Prerequisites or simultaneous courses
1 Numerical methods in linear algebra 3 _
2 Numerical solution of ordinary differential equations 3 Advanced numerical analysis
3 Numerical solution of integral equations 3 Advanced numerical analysis
4 Theory of integral equations 3 Real analysis
5 Numerical solution of partial differential equations 3 Numerical solution of partial differential equations
6 Finite element method 3 Advanced numerical analysis, Real analysis
7 Approximation theory 3 Advanced numerical analysis, Real analysis
8 Wavelets and their application 3 Real analysis
9 Numerical solution of fractional differential and integral equations 3 Advanced numerical analysis
10 Numerical solution of stochastic differential equations 3 Numerical solution of stochastic differential equations
11 Interval analysis 3 Numerical methods in linear algebra
12 mathematical modeling
 
3 _
13 Meshless methods 3 Advanced numerical analysis
14 Special Topics in Numerical Analysis 3 Group permission
 

 
Optimization branch
Main Lessons:
 
No Course Units
1 Advanced linear optimization 3
2 Advanced nonlinear optimization 3
 
 
 
Optimization branch - Specialized optional courses: 
No Course Units Prerequisites or simultaneous courses
1 Dynamic programming 3  
2 Integer  programming 3  
3 Combinatorial optimization 3  
4 Stochastic optimization 3  
5 Advanced  linear optimization 2 3  
6 Advanced nonlinear semi-infinite optimization 2 3  
7 Linear semi-infinite optimization 3  
8 Multi objective optimization 3  
9 Network optimization 3  
10 Non-smooth optimization 3  
11 Optimization and neural networks 3  
12 Convex optimization 3  
13 Calculus of variations & optimal control 3  
14 Internal point methods 3  
15 Advanced simulation 3  
16 Stochastic optimal control 3  
17 Linear and nonlinear control 3  
18 Mathematical modeling 3  
19 Game theory and applications 3  
20 Facility location problem 3  
21 Special topics in optimization 3  
 

 
Coding and Cryptography
Main courses: 
Course No Course units
101 Algorithm and calculation 3
102 Information theory 3
 
 

 
Cryptography branch
Compulsory-optional courses: 
No Course Units Hours/ theory Hours/ applied Total hours Prerequisites or simultaneous courses
201* Cryptography 1 3 48   48 101 , 102
202 Cryptography 2 3 48   48 201
203 Network security 3 48   48 201
204 Probabilistic methods in  Cryptography 3 48   48 201
205 Steganography 3 48   48 101 , 102
206 Database security 3 48   48 201
207 Computational number theory 3 48   48 201
208 Cryptography protocols 3 48   48 201
209 Formal methods in Cryptography 3 48   48 201
210 Special topics in Cryptography 3 48   48 Group permission
*Passing the course 201 of this table is mandatory for the students whose majoring field is Cryptography .


 
Coding branch
Compulsory-optional courses
No Course Units Hours/ theory Hours/ applied Total hours Prerequisites or simultaneous courses
3o1* Coding theory 1 3 48   48 101,102
302 Coding theory 2 3 48   48 301
303 Network coding theory 3 48   48 301
304 Iterative decoding algorithm 3 48   48 302
305 Space time coding 3 48   48 301
306 Source coding 3 48   48 101
307 Quantum coding and information theory 3 48   48 301
308 Ring based codes 3 48   48 301
309 Linear error correcting network codes 3 48   48 303
310 Special topics in coding 3 48   48 Group permission
*Passing the course301 of this table is mandatory for the students whose majoring field is coding.

 
 
Mathematical finance branch
Main Courses:
 
No Course Units Hours/ theory Hours/ applied Total hours Prerequisites or simultaneous courses
1 Mathematical finance 1 3 48   48 Theory of probability and Stochastic calculus as simultaneous course
2 Stochastic calculus in finance 3 48   48 Measure theory and probability
 


Mathematical finance branch-Optional courses Courses: 
No Course Units Hours/ theory Hours/ applied Total hours Prerequisites or simultaneous courses
1 Mathematical finance 2 3 48   48  
2 Numerical methods in financial mathematics 3 48   48  
3 Stochastic differential equations for financial markets 3 48   48  
4 Semi martingales for financial markets 3 48   48  
5 Numerical solution of Stochastic differential equations 3 48   48  
6 Partial differential equations in mathematical finance 3 48   48 Measure theory and probability
7 Monte Carlo methods for finance 3 48   48  
8 Statistical methods for finance 3 48   48  
9 Risk variations and management 3 48   48  
10 Stochastic portfolio theory 3 48   48  
11 Financial time series 3 48   48  
12 Financial engineering 3 48   48  
13 Malliavin calculus and its applications in finance 3 48   48  
14 Levy processes in mathematical finance 3 48   48  
15 Operational risk 3 48   48  
16 Mathematics of investments 3 48   48  
17 High- dimensional data analysis 3 48   48  
18 Stochastic optimal control 3 48   48 Stochastic calculus in finance
19 Special topics in mathematical finance 3 48   48 Group permission
 
 
 
The branch of differential equations and dynamic systems
Selected Specialized Course Schedule:
 
No Course Units Prerequisites or simultaneous courses
1 Ordinary differential equations 2 3 Ordinary differential equations 1
2 Partial differential equations 2 3 Partial differential equations 1
3 Discrete dynamic systems 1 3 Fundamentals of Dynamic Systems (Undergraduates)
4 Individual theory 1 3 Preliminary theory of differential equations  (Undergraduates)
5 Dynamic systems 2 3 Dynamic systems 1
6 Variational  methods in differential equations 3 Partial differential equations 1
The student must choose at least one course from the courses in the table above.

 
Ordinary Differential Equations Branch
Selected Specialized Course Schedule:
Number The Name of Course Units Prerequisites or Corequisites
1 Sturm Liouville Theory 3 Ordinary Differential Equation 1
2 Integral Equations 3 Ordinary Differential Equation 1
3 Asymptotics Analysis 3 Complex Functions and Ordinary Differential Equation 1
4 Calculus of Variations 3  
5 Infinite Dimensional Dynamical Systems 3 Ordinary Differential Equation 1
6 Fractional Differential Equations 3 Complex Functions (BSc Course)
7 Delay Differential Equational 3 Dynamical Systems 1
8 Basic tools in differential Equations 3 Real Analysis 1
9 Special Topics in ODE 3 Groups’ Permission
 
 
Partial Differential Equations
Selected Specialized Course Schedule:
Number The Name of Course Units Prerequisites or Corequisites
1 Elliptic Equations 3 Partial Differential Equations 1
2 Applications of Lie group in Differential Equations 3 Partial Differential Equations 1
3 Semi-groups and Evolution Equations 3 Partial Differential Equations 1
4 Inverse Problems 3 Partial Differential Equations 1
5 Hyperbolic Functions 3 Partial Differential Equations 1
6 Mathematical Biology 3 Dynamical Systems 1
7 Control Theory 3 Dynamical Systems 1
8 Mathematical Physics 1 3 Real Analysis 1
9 Mathematical Physics 2 3 Real Analysis 1
10 Special Topics in PDE 3 Groups’ Permission


 
Dynamical Systems Branch
Selected Specialized Course Schedule:
Number The Name of Course Units Prerequisites or Corequisites
1 Ergodic Theory 3 Real Analysis 1
2 Complex Dynamics 3 Complex Function (BSc Course) with the permission of Professor
3 Theory of Limit Cycles 3 Dynamical Systems 1
4 Slow-Fast Systems and Canard Cycles in Plane 3 Dynamical Systems 1
5 Bifureations in Hamiltonian Systems 3 Dynamical Systems 1
6 Averaging and Normal Form theory 3 Dynamical Systems 1
7 Computational Methods in dynamic Systems 3 Dynamical Systems 1
8 Singularity Theory 2 3 Singularity Theory 1
9 Equivariant Dynamics 3 Basic Theory of Differential Equations (Bachelor Course) and Foundation of Algebra (Bachelor Course)
10 Special Topics in Dynamical Systems 3 Groups’ Permission
The student is required to take at least one lesson from the set of tables in Tables 3, 4 and 5
Note: The student must take a maximum of one of the related master's degree courses outside of tables 2 to 5 in the opinion of the group. 


 



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