Table of courses for Graduate Program of Applied Mathematics

 | Post date: 2021/06/16 | 
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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