Course Aim: Introduce students to basic concepts of graph theory, graph properties and formulations of typical graph problems. This is also supplemented with some abstract-level algorithms for the presented problems and with some advanced graph theory topics.
Main Topics: The Basics and definitions of graph theory - graphs and their relatives - isomorphism and automorphism of graphs - degree sequences and edge counting - eulerian and hamiltonian walks/cycles -trees and networks - traveling salesman problem (TSP) - graph matchings- euler's formula - networks flows - graph colorings - combinatorial objects and techniques - sets and subsets- sequences - basic principles of counting- permutations and factorials - fibonacci numbers- catalan numbers – inclusion – exclusion - recursions - pigeonhole principle- estimations - algebraic combinatorics: binomial coefficients - pascal's triangle - geometric combinatorics.
Main Topics: The Basics and definitions of graph theory - graphs and their relatives - isomorphism and automorphism of graphs - degree sequences and edge counting - eulerian and hamiltonian walks/cycles -trees and networks - traveling salesman problem (TSP) - graph matchings- euler's formula - networks flows - graph colorings - combinatorial objects and techniques - sets and subsets- sequences - basic principles of counting- permutations and factorials - fibonacci numbers- catalan numbers – inclusion – exclusion - recursions - pigeonhole principle- estimations - algebraic combinatorics: binomial coefficients - pascal's triangle - geometric combinatorics.
Course Aim: Introduce students to probability and statistics fundamentals.
Main Topics: Probability axioms - conditional probability - the law of total probability - Bayes’theorem – independence - discrete and continuous random variables - multiple random variables - sum of random variables - sample mean – statistical inference - testing - estimation - confidence statements.
Main Topics: Probability axioms - conditional probability - the law of total probability - Bayes’theorem – independence - discrete and continuous random variables - multiple random variables - sum of random variables - sample mean – statistical inference - testing - estimation - confidence statements.
Course Aim: Introduce students to the foundations of discrete Structures.
Main Topics: Big-O - counting methods - recursion/recurrences - Elementary logic including propositional/predicate logic - methods of proof – relations - basic definitions and properties - special types of relations - Boolean algebras - introduction to graph theory - special types of graphs -trees and their applications - practice in reasoning formally and proving theorems.
Main Topics: Big-O - counting methods - recursion/recurrences - Elementary logic including propositional/predicate logic - methods of proof – relations - basic definitions and properties - special types of relations - Boolean algebras - introduction to graph theory - special types of graphs -trees and their applications - practice in reasoning formally and proving theorems.
Course Aim: Acquire the basic knowledge and understating of a core of analysis for calculus and algebra.
Main Topics: Solving equations/inequalities and notion of functions, Monotonicity of functions and function graphing, limits, continuity and differentiability, differentiation rules and meaning of differentiation, indefinite/definite integrals, Integration techniques, Vectors and matrices, Determinants and cross product
Main Topics: Solving equations/inequalities and notion of functions, Monotonicity of functions and function graphing, limits, continuity and differentiability, differentiation rules and meaning of differentiation, indefinite/definite integrals, Integration techniques, Vectors and matrices, Determinants and cross product
Course Aim: Develop practical skills about using fundamental principles to solve physics quantitative problems.
Main Topics: Vector analysis: velocity, acceleration, forces, work, and energy - Linear and Angular momentum - Rotational motion - Dynamics of rigid body - Moment of inertia - Simple Harmonic Motion - Structure of materials and elasticity.
Main Topics: Vector analysis: velocity, acceleration, forces, work, and energy - Linear and Angular momentum - Rotational motion - Dynamics of rigid body - Moment of inertia - Simple Harmonic Motion - Structure of materials and elasticity.
Course Aim: Develop students’ practical skills in differential calculus of single variable functions.
Main Topics: Types of functions, curve sketching using shifts, reflections, and scaling for: polynomials, radical functions, equation of the straight line, exponential functions and logarithmic function. Solving equations involving exponentials and logarithms- Trig functions and inverse trig functions- Hyperbolic functions and Inverse Hyperbolic functions- Limits and Continuity- Differentiation using definition and rules- Derivatives of inverse trig and hyperbolic functions- Higher order derivatives- Logarithmic differentiation- Implicit differentiation- Linear approximation- L’Hopital’s Rule- Absolute and Local Extrema- Monotonicity and Concavity of a function- Optimization- Introducing the concept of Antiderivative, indefinite integral, basic rules of integration- Definite integrals and Fundamental Theorem of Calculus- Integration by substitution- Application to integration: Area bounded between curves
Main Topics: Types of functions, curve sketching using shifts, reflections, and scaling for: polynomials, radical functions, equation of the straight line, exponential functions and logarithmic function. Solving equations involving exponentials and logarithms- Trig functions and inverse trig functions- Hyperbolic functions and Inverse Hyperbolic functions- Limits and Continuity- Differentiation using definition and rules- Derivatives of inverse trig and hyperbolic functions- Higher order derivatives- Logarithmic differentiation- Implicit differentiation- Linear approximation- L’Hopital’s Rule- Absolute and Local Extrema- Monotonicity and Concavity of a function- Optimization- Introducing the concept of Antiderivative, indefinite integral, basic rules of integration- Definite integrals and Fundamental Theorem of Calculus- Integration by substitution- Application to integration: Area bounded between curves