


MEHRANS. FALLAH


Courses

Aims 
Discrete Mathematics(SPRING_2017) * Counting Principles: Principles of sum a and product, arrangement, permutation, combination, combination with repetition, the reflection principle * Inclusion and Exclusion: Theorem of the principle of inclusion and exclusion, applications in counting, generalization of the principle * Generating Functions: The generating function of a given sequence, the application of generating functions in counting problems, the convolution of sequences * Logic: Introduction, propositional logic, semantics and model theory, proof theory * FirstOrder Logic: Open statements, quantifiers, model theory, proof theory, soundness, completeness * Properties of Integers: The axiomatic system of integers, mathematical induction, generalizations, inductive definitions, applications * Elementary Number Theory: Divisibility, greatest common divisor, division algorithm, the fundamental theorem of arithmetics * Residues: The complete system of residues, the residues system of residues, Eulers phi function, Lagranges theorem, EulerFermats theorem, Chinese residues * Relations and Functions: Onetoone functions, images, onto functions, restriction * Partially Ordered Sets: Reflexive, symmetric, antisymmetric, and transitive relations, equivalence relations, commutative and associative relations, minimal and maximal, lower and upper bounds, supremums, infimums, lattice * Recurrences: Recursive equations, solving linear homogeneous recursive equations * Nonhomogeneous Recursive Equations: Solution, using generating functions, system of equations * Graph Theory: Undirected and directed graphs, walks, paths, circuits, cycles, Eulerian graphs * Hamiltonian and Planar Graphs: Definitions, Theorems * Graph coloring: Chromatic polynomials, chromatic numbers, decomposition theorem

To acquaint students with mathematical structures and their application in computer engineering and science 
Discrete Mathematics(SPRING_2017) * Counting Principles: Principles of sum a and product, arrangement, permutation, combination, combination with repetition, the reflection principle * Inclusion and Exclusion: Theorem of the principle of inclusion and exclusion, applications in counting, generalization of the principle * Generating Functions: The generating function of a given sequence, the application of generating functions in counting problems, the convolution of sequences * Logic: Introduction, propositional logic, semantics and model theory, proof theory * FirstOrder Logic: Open statements, quantifiers, model theory, proof theory, soundness, completeness * Properties of Integers: The axiomatic system of integers, mathematical induction, generalizations, inductive definitions, applications * Elementary Number Theory: Divisibility, greatest common divisor, division algorithm, the fundamental theorem of arithmetics * Residues: The complete system of residues, the residues system of residues, Eulers phi function, Lagranges theorem, EulerFermats theorem, Chinese residues * Relations and Functions: Onetoone functions, images, onto functions, restriction * Partially Ordered Sets: Reflexive, symmetric, antisymmetric, and transitive relations, equivalence relations, commutative and associative relations, minimal and maximal, lower and upper bounds, supremums, infimums, lattice * Recurrences: Recursive equations, solving linear homogeneous recursive equations * Nonhomogeneous Recursive Equations: Solution, using generating functions, system of equations * Graph Theory: Undirected and directed graphs, walks, paths, circuits, cycles, Eulerian graphs * Hamiltonian and Planar Graphs: Definitions, Theorems * Graph coloring: Chromatic polynomials, chromatic numbers, decomposition theorem

To acquaint students with mathematical structures and their application in computer engineering and science 
Formal Models & Information Security(SPRING_2017) * Introduction: Formal methods and their application in analyzing systems, advantages and shortcomings * Discretionary access control models and the safety problem, the HRU model * Mandatory access control models: advantages and shotcomings, the problem of covert channels, the need for informationflow models * Noninterference in deterministic and nondeterministic systems * Applied flow model and probabilistic noninterference * Quantified information flow * Approximate noninterference, refining noninterference, downgrading * Languagebased implementation of noninterference * Categorizing security properties and policies: a topological approach * Categorizing security properties and policies: a process algebraic approach * Analysis and verification of security protocols: a classification of existing approaches * Example vulnerable protocols, the DolevYao model * Analyzing authentication protocols using modal logics * The agreement problem in authentication protocols * Model checking and the analysis of security protocols

A formal approach to information security systems 
Design of Programming Language(FALL_2016)


Information Security S. C.(FALL_2016)


Software Systems Security(FALL_2016) * Software Security * Security Vulnerabilities * Secured and Safe Programming * Security Requirements Analysis * Threat Modeling and Risk Analysis * Security Review and Auditing 1 * Security Review and Auditing 2 * Review and Auditing Tools * Security Test Plans * Security Test Cases * Fuzz Testing * Fault Injection * Languagebased Security * Security in Mobile Applications * Security in WebFacing Applications

The course acquaint the students with major challenges in designing and implementing secure software systems and application programs, programs that are not vulnerable to malicious attacks. The student will learn why security is important, what kinds of vulnerabilities may exist in software, how one may exploit the vulnerabilities, and how attacks can be defeated systematically through building security in the software development lifecycle. 
Discrete Mathematics(SPRING_2016) * Counting Principles: Principles of sum a and product, arrangement, permutation, combination, combination with repetition, the reflection principle * Inclusion and Exclusion: Theorem of the principle of inclusion and exclusion, applications in counting, generalization of the principle * Generating Functions: The generating function of a given sequence, the application of generating functions in counting problems, the convolution of sequences * Logic: Introduction, propositional logic, semantics and model theory, proof theory * FirstOrder Logic: Open statements, quantifiers, model theory, proof theory, soundness, completeness * Properties of Integers: The axiomatic system of integers, mathematical induction, generalizations, inductive definitions, applications * ٍElementary Number Theory: Divisibility, greatest common divisor, division algorithm, the fundamental theorem of arithmetics * Residues: The complete system of residues, the residues system of residues, Eulers phi function, Lagranges theorem, EulerFermats theorem, Chinese residues * Relations and Functions: Onetoone functions, images, onto functions, restriction * Partially Ordered Sets: Reflexive, symmetric, antisymmetric, and transitive relations, equivalence relations, commutative and associative relations, minimal and maximal, lower and upper bounds, supremums, infimums, lattice * Recurrences: Recursive equations, solving linear homogeneous recursive equations * Inhomogeneous Recursive Equations: Solution, using generating functions, system of equations * Graph Theory: Undirected and directed graphs, walks, paths, circuits, cycles, Eulerian graphs * Hamiltonian and Planar Graphs: Definitions, Theorems * Graph coloring: Chromatic polynomials, chromatic numbers, decomposition theorem

To acquaint students with mathematical structures and their application in computer engineering and science 
Discrete Mathematics(SPRING_2016) * Counting Principles: Principles of sum a and product, arrangement, permutation, combination, combination with repetition, the reflection principle * Inclusion and Exclusion: Theorem of the principle of inclusion and exclusion, applications in counting, generalization of the principle * Generating Functions: The generating function of a given sequence, the application of generating functions in counting problems, the convolution of sequences * Logic: Introduction, propositional logic, semantics and model theory, proof theory * FirstOrder Logic: Open statements, quantifiers, model theory, proof theory, soundness, completeness * Properties of Integers: The axiomatic system of integers, mathematical induction, generalizations, inductive definitions, applications * ٍElementary Number Theory: Divisibility, greatest common divisor, division algorithm, the fundamental theorem of arithmetics * Residues: The complete system of residues, the residues system of residues, Eulers phi function, Lagranges theorem, EulerFermats theorem, Chinese residues * Relations and Functions: Onetoone functions, images, onto functions, restriction * Partially Ordered Sets: Reflexive, symmetric, antisymmetric, and transitive relations, equivalence relations, commutative and associative relations, minimal and maximal, lower and upper bounds, supremums, infimums, lattice * Recurrences: Recursive equations, solving linear homogeneous recursive equations * Inhomogeneous Recursive Equations: Solution, using generating functions, system of equations * Graph Theory: Undirected and directed graphs, walks, paths, circuits, cycles, Eulerian graphs * Hamiltonian and Planar Graphs: Definitions, Theorems * Graph coloring: Chromatic polynomials, chromatic numbers, decomposition theorem

To acquaint students with mathematical structures and their application in computer engineering and science 
Formal Models & Information Security(SPRING_2016) * Introduction: Formal methods and their application in analyzing systems, advantages and shortcomings * Discretionary access control models and the safety problem, the HRU model * Mandatory access control models: advantages and shotcomings, the problem of covert channels, the need for informationflow models * Noninterference in deterministic and nondeterministic systems * Applied flow model and probabilistic noninterference * Quantified information flow * Approximate noninterference, refining noninterference, downgrading * Languagebased implementation of noninterference * Categorizing security properties and policies: a topological approach * Categorizing security properties and policies: a process algebraic approach * Analysis and verification of security protocols: a classification of existing approaches * Example vulnerable protocols, the DolevYao model * Analyzing authentication protocols using modal logics * The agreement problem in authentication protocols * Model checking and the analysis of security protocols

A formal approach to information security systems 
Design of Programming Language(FALL_2015)


Information Security S. C.(FALL_2015)













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