




Courses

Elementary Number Theory(SPRING_2018)
Aims:
knowing elementry results in number theory
Syllabus:
 divisibility and g.c.d
 prime numbers
 congruence
 primitive root
Text Book:

Finite Groups(SPRING_2018)
Aims:
to know the structure of groups
Syllabus:
 action of groups
 Sylow subgrous and its theorems
 direct product of groups
 semi direct product of groups
 solvable and nilpotent groups
 transfer homomorphism
Text Book:
 theory of groups, alireza jamali
 Theory of finite groups, Isaacs

Foundations of Combinatorics(SPRING_2018)
Aims:
Foundamental and Basic concept of combinatorial mathematics
Syllabus:
 Counting concept such as selection,arrangement and binomial coefficient
 Inclusion and exclusion principle
 Generating function
 Recurrence relation
 Definition of graphs, Cycle, Path, complete graph, graph isomorphism and vertex degree
 Eulerian trail
 Tree, bipartite graph, planer graph
 Hamiltonian path and cycle
 Matrices and its combinatorial properties
 Latin square
 Magic square and System of distinct representative and Philip Hall theorem
 Block design and Steiner triple System
 Hadamard matrices
Text Book:
 I. Anderson, A first course in combinatorial mathematics
 R.P. Grimaldi, Discrete and combinatorial mathemat,ics, an applied introduction
 Introduction to combinatorial theory, R,C. Bose and B. Manvel

Algebra(FALL_2017)
Aims:
studying Galois theory and constructing a square with the same area as a given circle by using only a finite number of steps with compass and straightedge
Syllabus:
 Action of groups
 Sylow Theorems
 Solvable groups and nilpotent groups and Normal series
 polynomial rings
 Unique factorization domain
 Irreducible tests
 Field extension
 Drawing by ruler and compass
 Splitting Field
 Galois correspondence
Text Book:
 A coursein algebra, Hungerfurd

Foundations of Combinatorics(FALL_2017)
Aims:
Foundamental and Basic concept of combinatorial mathematics
Syllabus:
 Counting concept such as selection,arrangement and binomial coefficient
 Inclusion and exclusion principle
 Generating function
 Recurrence relation
 Definition of graphs, Cycle, Path, complete graph, graph isomorphism and vertex degree
 Eulerian trail
 Tree, bipartite graph, planer graph
 Hamiltonian path and cycle
 Matrices and its combinatorial properties
 Latin square
 Magic square and System of distinct representative and Philip Hall theorem
 Block design and Steiner triple System
 Hadamard matrices
Text Book:
 I. Anderson, A first course in combinatorial mathematics
 R.P. Grimaldi, Discrete and combinatorial mathemat,ics, an applied introduction
 Introduction to combinatorial theory, R,C. Bose and B. Manvel

Math. (I)(FALL_2017)
Aims:
Introduction to complex numbers differential and Integral Calculus for one variable functions
Syllabus:
 Complex numbers
 Limit and Continuity
 Differentition
 transcendental functions
 Integration
 Integrations Technique
 Application of Integration
 Sequence and series and Power series
Text Book:
 Calculus: A complete Course by Adams

Special Topics(FALL_2017)
Aims:
learning developed theorem on theory of finite groups
Syllabus:
 Direct product of groups
 semi direct product
 nilpotent groups
 solvable groups
 transfer homomorphism
 theorems on split extension
 pnilpotent and psolvable groups
 action of a group on a group
 cohomology of a group
Text Book:

Algebra(SPRING_2017)
Aims:
studying Galois theory and constructing a square with the same area as a given circle by using only a finite number of steps with compass and straightedge
Syllabus:
 Action of groups
 Sylow Theorems
 Solvable groups and nilpotent groups and Normal series
 polynomial rings
 Unique factorization domain
 Irreducible tests
 Field extension
 Drawing by ruler and compass
 Splitting Field
 Galois correspondence
Text Book:
 A coursein algebra, Hungerfurd

Math. (II)(SPRING_2017)
Aims:
Introduction to Deferential and Integral of multivariate functions
Syllabus:
 Curves and vector functions
 Multivariate functions and partial derivative
 Application of partial derivative
 multiple Integral
 Vector field
 Vector analyzes
 linear algebra
Text Book:
 Calculuse a complete course, Rabert. A. Adams

Foundations of Combinatorics(FALL_2016)
Aims:
Foundamental and Basic concept of combinatorial mathematics
Syllabus:
 Counting concept such as selection,arrangement and binomial coefficient
 Inclusion and exclusion principle
 Generating function
 Recurrence relation
 Definition of graphs, Cycle, Path, complete graph, graph isomorphism and vertex degree
 Eulerian trail
 Tree, bipartite graph, planer graph
 Hamiltonian path and cycle
 Graph coloring and chromatic polynomial
 Matrices and its combinatorial properties
 Latin square
 Magic square and System of distinct representative and Philip Hall theorem
 Block design and Steiner triple System
 Hadamard matrices
Text Book:
 I. Anderson, A first course in combinatorial mathematics
 R.P. Grimaldi, Discrete and combinatorial mathemat,ics, an applied introduction
 Introduction to combinatorial theory, R,C. Bose and B. Manvel

Foundations of Combinatorics(FALL_2016)
Aims:
Foundamental and Basic concept of combinatorial mathematics
Syllabus:
 Counting concept such as selection,arrangement and binomial coefficient
 Inclusion and exclusion principle
 Generating function
 Recurrence relation
 Definition of graphs, Cycle, Path, complete graph, graph isomorphism and vertex degree
 Eulerian trail
 Tree, bipartite graph, planer graph
 Hamiltonian path and cycle
 Graph coloring and chromatic polynomial
 Matrices and its combinatorial properties
 Latin square
 Magic square and System of distinct representative and Philip Hall theorem
 Block design and Steiner triple System
 Hadamard matrices
Text Book:
 I. Anderson, A first course in combinatorial mathematics
 R.P. Grimaldi, Discrete and combinatorial mathemat,ics, an applied introduction
 Introduction to combinatorial theory, R,C. Bose and B. Manvel

Math. (I)(FALL_2016)
Aims:
Introduction to complex numbers differential and Integral Calculus for one variable functions
Syllabus:
 Complex numbers
 Limit and Continuity
 Differentition
 transcendental functions
 Integration
 Integrations Technique
 Application of Integration
 Sequence and series and Power series
Text Book:
 Calculus: A complete Course by Adams












© AUT All rights reserved.
AUT is not responsible for the content of external sites. 


424 Hafez Ave, Tehran, Iran, 158754413. +98 (21) 64540






