Dr. Jean Nicolas Pestieau

Assistant Professor – Mathematics

Suffolk County Community College

Eastern Campus

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Shinnecock 223

pestiej@sunysuffolk.edu

(631) 548-3585

 

 

 

 

   

The Sacks spiral, a number spiral devised by Robert Sacks in 1994, reveals the distribution of the primes.

[click here to read more about the Sacks spiral]

 

 

 

       MAT101 – A Survey of Mathematical Reasoning   [Course Outline – Day Class] [List of homework problems]

 

 

Set Theory                          

 

Here are two interesting questions related to infinite sets.

 

    How big is infinity?  These introductory notes shed some light on the arithmetic of transfinite cardinals. 

This presentation introduces the formalism behind the quantification of infinities.

 

    How can one ball be cut to yield two identical balls?  The Tarski-Banach paradox is a striking illustration

of the strange properties of infinite sets.

 

[Extra-credit assignment]

[Exam 1]

 

 

Logic                                                            

[Exam 2]

           

    What is the implication of implication? Here is how the famed mathematician Timothy Gowers answers this tricky

question.

 

                        [Assignment 3 – The conditional + circuits]                    

                        Assignment 4 – Arguments]                      

                        [Extra-credit assignment - Logical puzzles + arguments from Alice in Wonderland]

                                                                       

                        [Sample final exam]

 

 

Mathematical Induction

 

    What is mathematical induction?  These notes present a quick overview of this principle.

 

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       MAT102 – A Survey of Contemporary Mathematical Topics   [Course Outline]

                                                                                     

 

Number Theory     

           

[Assignment 1]

 

 

Combinatorics & Probability      

 

    Here are the probabilities of poker hands.

           

[Assignment 2]

           

 

Non-Euclidian Geometry

           

Below are two chapters from Timothy Gowers’s Mathematics: A Very Short Introduction (Oxford).       

 

    Here is his chapter on Dimension.

    Here is his chapter on Geometry.

 

 

Graph Theory

 

[Assignment 3]

[Assignment 4]

 

Graph theory can be used to solve old problems in the standard framework of Euclidian geometry.

 

  This presentation shows the existence proof of the five platonic solids using graphs.

 

 

Group Theory

                                                           

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       MAT007 – Algebra I   [Course Outline]

 

The Basics

Linear Equations and Inequalities  

     Graphing                             

            Systems of Linear Equations

Polynomials I – Operations

Polynomials II - Factoring

            Rational Expressions

      Roots and radicals           

                            

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       MAT111 – Algebra II   [Course Outline]

 

Elementary Algebra Review

Linear Equations and Inequalities in One Variable

     Linear Equations and Inequalities in Two Variables

      Systems of Linear Equations and Inequalities

      Polynomials and Exponents

      Rational Expressions

      Rational Exponents and Roots

      Quadratic Equations        

         

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       MAT121 – Finite Mathematics   [Course Outline] [List of homework problems]

 

Introduction to Matrix Algebra

Game Theory                     

Markov Chains       

Systems of Linear Equations

Linear Programming

                         

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       MAT124 – Fundamentals of Precalculus I   [Course Outline] [List of homework problems]

 

Functions and Their Graphs

            Polynomial and Rational Functions

            Exponential and Logarithmic Functions

            Introduction to Trigonometric Functions

                                               

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       MAT131 – Calculus for Non-Science Majors   [Course Outline] [List of homework problems]

 

Algebraic and Pre-Calculus Review

 

Linear and Nonlinear Models

 

Introduction to the Derivative

                        Limits

                        The Derivative: Definitions                                 

                                    [Exam 1]

                       

Differentiation: Techniques and Applications

                        Sum and Constant Multiple Rules

Marginal Analysis  

Product and Quotient Rules

[Exam 2]

The Chain Rule

Derivatives of Logarithmic and Exponential Functions     

 

Applications of the Derivative

                        Finding Extrema Points and the First-Derivative Test                                

Optimization Problems

                        Analyzing Graphs and the Second-Derivative Test

Related Rates

                        Elasticity      

                                    [Exam 3]

                       

Introduction to the Integral

            The Indefinite Integral                              

            The Definite Integral and the Fundamental Theorem of Calculus                                   

                                    [Take-Home Exam 4]

 

                                    [Sample Final Exam]

 

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       MAT141 – Calculus with Analytic Geometry I   [Course Outline]

 

Limits and Continuity

The Derivative

Applications of the Derivative

The Differential and Antiderivative

The Definite Integral

Applications of the Definite Integral