TEACHING :

 

I will be teaching "Math 111" and “Math 261” in the Second Semester of 2016/2017.

Previously, I taught:

Students can get old (First, Second, and Final) exams for Calculus A, Calculus B, and Linear Algebra (and some other courses) in the Past Exams.

Students are welcome to meet with me in person at any time I am in the office. For my office hours, see here.

Math 101 - Calculus A

Math 102 - Calculus B

Math 111 - Linear Algebra

This course will cover the following subjects:

Limits, Continuous functions. The derivative, formulas of differentiation, differentials. Related rates, Extrema. Rolle’s and mean value theorems. Graph sketching Optimization. Indefinite integrals, definite integrals, fundamental theorem of calculus. Applications of definite integrals to find area, volume and arc length.


Once a student pass this class, he/she will be able to:

  1. Analyze and manipulate functions and sketch the graph of a function in a systematic way.

  2. Differentiate function by applying standard rules.

  3. Evaluate integrals by means of standard techniques of integration and method of substitution.

  4. Achieve the level of mathematical understanding required for studying calculus B (Math 102) .

This course will cover the following subjects:

Logarithmic and exponential functions. Inverse trigonometric and hyperbolic functions. Techniques of integration. Indeterminate forms and improper integrals. Conic sections. Plane curves and polar coordinates. Vectors and surfaces in R3.


Once a student pass this class, he/she will be able to:

  1.     Work with some new functions in mathematics and use them for studying phenomena that are investigated in physics, engineering, biology, etc.

  2.     Evaluate a large class of integrals and apply them for calculating lengths of curves and areas of plane regions.

  3.     Get images of simple configurations of points in the plane and space, and they will be able to find their basic properties.

This course will cover the following subjects:

Matrices: matrix operations, inverse of a matrix, solving systems of linear equations. Determinants: definition and properties, cofactor expansion and applications. Vectors in R2 and R3 , scalar and cross products, lines and planes, applications. The vector space Rn . subspaces, linear independence, basis and dimensions, orthogonality. Gram-Schmidt orthogonalization process. Rank of matrix. Eigenvalues and eigenvectors, diagonalization of a matrix.


Once a student pass this class, he/she will be able to:

  1. Understand the role of matrices and vectors principles in various settings of life.

  2. Apply the basic vectors and matrix operations in solving linear systems and matrix eigenproblems.

  3. Apply some techniques in constructing and finding a basis for some subspaces and computing their dimensions.

  4. Familiarize some matrix spaces (row space, column space, null space and eigenspace) and their dimensions (kernel and nullity) .

  5. Compute the eigenpairs of a matrix and their relationship with the existence of the inverse of the matrix and linear independence of the eigenvectors.

Math 250 - Introduction to Foundations of Mathematics

This course will cover the following subjects:

Algebra of propositions, mathematical induction, operations on sets, binary relations, equivalence relations and partitions, denumerable sets, Cardinal numbers, partial order. Boolean algebra.



Once a student pass this class, he/she will be able to:

   The student is familiarized with the essential logical and set-theoretic tools that will be utilized in subsequent pure mathematics courses, most notably in abstract algebra, real and complex analysis, and topology.

  1. Lecture Notes of Foundations of Mathematics, by Abdullah AlAzemi.

       

   
  Past exams for the students of Foundations of Mathematics: Past Exams.
 

Math 261 - Introduction to Abstract Algebra

This course will cover the following subjects:

Groups and their basic properties; subgroups; permutation groups; Lagrange’s Theorem; direct product of groups; factor groups ; group homomorphism; rings; integral domains; fields; ring homomorphism; ideals; factor rings ; polynomial rings.

More about this course can be found here.

  1. Lecture Notes of Abstract Algebra, by Abdullah AlAzemi.

  2. Revision for the Final Exam.

  3. Past exams for the students of Abstract Algebra: Past Exams.