Masoud Ataei

My Curriculum Vitae (CV) (last update 2015)

Education:

MSc in Computer Science
London, ON. Canada Sept 2016 - Dec 2017
Supervisor: Prof. Marc Moreno Maza
Research group: www.metafork.org

PhD in Mathematics
London, ON, Canada, Sept 2011 - Aug 2015
Thesis: "Galois 2-extensions"
Supervisor: Prof. Jan Minac
Co-Supervisor: Prof. Eric Schost

MSc in Mathematics
Zanjan, Iran, 2008 - 2010.
Thesis: "On Maximal Curves over Finite Fields"

BSc in Mathematics
Tehran, Iran, 2003 - 2008.


Research Interest in Computer Science:

Solving system of non-linear equations, inequations and inequalities using Cylindrical Algebraic Decomposition algorithm, decomposition of semi-algebraic sets, real root isolation, quantifier elimination

Research Interest in Mathematics:

Galois Realization of Finite Groups with Restricted Ramification, Embedding Problem of finite Groups, Tower of Algebraic Function Fields over Finite Fields with Many Rational Places, Galois Tower of Global Fields, Point Counting of Algebraic Curves over Finite Fields


Link to Conferences:

Interesting free books and lecture notes:

Algebraic Number Theory  MIT

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Let's Play Soccer: Photo 1, Photo 2, Photo 3.
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Contact Info:
Room 105
Deparment of Mathematics
Middlesex College
Western University
London, ON.

Email:
mataeija at uwo dot ca
msd.ataei at gmail dot com









Teaching:


I currently teach Elementary Linear Algebra (Math1229A) in Huron College (Fall term) and Western University (Summer term):

Math1229A - Elementary Leaner Algebra -- Course Outline
                                                               -- Assignment 1
                                                               -- Assignment 2
                                                               -- Assignment 3
                                                               -- Midterm 1 (Summer 2016)
                                                               -- Midterm 2 (Summer 2016)
                                                               -- Final (Summer 2016)

Interesting paper related to Linear Algebra:
 The $25,000,000,000 Eigenvector: The Linear Algebra Behind Google

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In Fall 2014, I was TA for courses Math 2124b and Math 3150b. Here is the instructor homepage.


Math 2124B - Introduction to Mathematical Problem Solving --- Course Outline
                                                                                                                    --- First Homework
                                                                                       --- First Homework Solutions
                                                                                       --- Second Homework
                                                                                       --- Second Homework Solutions  [Correction Exercise 7(b)]


Math 3150B
- Elementary Number Theory                       --- Course Outline
                                                                             --- First Homework
                                                                             --- First Homework Solutions
                                                                             --- Second Homework
                                                                             --- Second Homework Solutions



Here are some interesting links and examples:

  • Polynomial  x^3+x+1 over GF(2) is an irreducible polynomial, the elements of GF(2^3)--written 0, x^0, x^1, ...--can be represented as polynomials with degree less than 3. For instance, (Reference: Wolfram)
x^3=-x-1=x+1

x^4=x(x^3)=x(x+1)=x^2+x

x^5=x(x^2+x)=x^3+x^2=x^2-x-1=x^2+x+1

x^6=x(x^2+x+1)=x^3+x^2+x=x^2-1=x^2+1

x^7=x(x^2+1)=x^3+x=-1=1=x^0.
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Do you like prime numbers? Do you like to know how hard working people succeed? so click here. (Yitang Zhang)

AMS:

People in Number Theory:
Bernoulli Number Website
Bernoulli Polynomials
            
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Computational example of Legendre Symbol: (Reference: Wikipedia)

\begin{align} \left ( \frac{12345}{331}\right )&=\left ( \frac{3}{331}\right ) \left ( \frac{5}{331}\right ) \left ( \frac{823}{331}\right ) \\ &= \left ( \frac{3}{331}\right ) \left ( \frac{5}{331}\right ) \left ( \frac{161}{331}\right ) \\ &= \left ( \frac{3}{331}\right ) \left ( \frac{5}{331}\right ) \left ( \frac{7}{331}\right ) \left ( \frac{23}{331}\right ) \\ &= (-1)\left (\frac{331}{3}\right) \left(\frac{331}{5}\right) (-1) \left(\frac{331}{7}\right) (-1)\left (\frac{331}{23}\right ) \\ &= -\left ( \frac{1}{3}\right ) \left ( \frac{1}{5}\right ) \left ( \frac{2}{7}\right ) \left ( \frac{9}{23}\right )\\ &= -\left ( \frac{1}{3}\right ) \left ( \frac{1}{5}\right ) \left ( \frac{2}{7}\right ) \left ( \frac{3^2}{23}\right )\\ &= -(1) (1) (1) (1) \\ &= -1. \end{align}

Or using a more efficient computation:

\left ( \frac{12345}{331}\right )=\left ( \frac{98}{331}\right )=\left ( \frac{2 \cdot 7^2}{331}\right )=\left ( \frac{2}{331}\right )=(-1)^\tfrac{331^2-1}{8}=-1.

The article Jacobi symbol has more examples of Legendre symbol manipulation.



 
      http://www.britannica.com/EBchecked/topic/62591/Daniel-Bernoulli
                  

Blaise Pascal:
    
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