TEACHING :
TEACHING :
I will be teaching "Math 226" and “Math 261” in the Second Semester of 2017/2018.
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:
✴Analyze and manipulate functions and sketch the graph of a function in a systematic way.
✴Differentiate function by applying standard rules.
✴Evaluate integrals by means of standard techniques of integration and method of substitution.
✴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:
✴ Work with some new functions in mathematics and use them for studying phenomena that are investigated in physics, engineering, biology, etc.
✴ Evaluate a large class of integrals and apply them for calculating lengths of curves and areas of plane regions.
✴ 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:
✴Understand the role of matrices and vectors principles in various settings of life.
✴Apply the basic vectors and matrix operations in solving linear systems and matrix eigenproblems.
✴Apply some techniques in constructing and finding a basis for some subspaces and computing their dimensions.
✴Familiarize some matrix spaces (row space, column space, null space and eigenspace) and their dimensions (kernel and nullity) .
✴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 111: Lecture Notes of Linear Algebra, by Abdullah AlAzemi,
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.
✴ Math 250: Lecture Notes of Foundations of Mathematics, by Abdullah AlAzemi.
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.
✴ Math 261: Lecture Notes of Abstract Algebra, by Abdullah AlAzemi.
• Past exams for the students of Abstract Algebra: Past Exams.
✴ Math 363: Lecture Notes of Advanced Linear Algebra, by Abdullah AlAzemi,
Math 226 - Euclidean Plane Geometry
This course has been designed to fill in a serious gap the preparation of future mathematics teachers, namely the lack of sound geometrical knowledge.
The course provide a comparative study of the geometry of the Euclidean plane using the following three approaches:
1. The classical Euclidean approach.
2. The analytic approach.
3. The transformations approach.
More about this course can be found here.
Math 363 - Advanced Linear Algebra
Linear algebra is a fundamental branch of mathematics and an essential part of the background required of mathematicians, engineers, physicists and other scientists. This is a second course in linear algebra, where the main objective is the careful treatment of the principle topics of linear algebra that
emphasis axiomatic development, proof and conceptual understanding rather than calculation; and
within this context, the course aims to:
1. Study abstract vector spaces, the correct general setting for understanding linear systems.
2. Develop tools for understanding and analyzing linear transformations, the means by which one relates objects from different vector spaces. This involves developing the classical theory of matrices,
determinants, and the study of the diagonalization problem of a linear transformation.
3. Introduce the concept of inner product on a vector space and study the associated ideas of orthogonal bases, self-adjoint and normal transformations (matrices) and the properties of their eigenvalues and eigenvectors, and orthogonal diagonalization of normal transformations (Spectral Theorem).
More about this course can be found here.
✴ Math 226: Lecture Notes of Euclidean Plane Geometry, by Abdullah AlAzemi.