My teaching philosophy can be summarized in the following few words, learning is a journey from point A to point B, where the teacher should provide clear guidance to his students during their learning journey. In this journey, the teacher should know exactly where it starts and where it ends, and the steps of the learning process must be very clear and well defined in his mind. Thus, I consider knowing the outcomes of the learning process is a crucial step. To avoid confusion and disappointment, these outcomes must be tangible and measurable to enable the evaluation of the whole process while happening and at the end. According to my philosophy, I am always keen that my students acquire the problem-solving skill, grasp the fundamental concepts and comprehend the reasoning of these concepts, work collaboratively and think critically That?s why I believe that the teacher must have deep knowledge about the topics of the course and be up-to-date about the advancements in the field.
In my teaching style, I always focus on how to prepare students to grabs the main concepts of a particular subject. Then I move to the details that allow them to make connections between these main concepts. My solid mathematical background provided me with a sense of logic, consistency, and comprehensiveness of my teaching style. This allowed me to communicate the main ideas combined with the required level of details that suits the mindsets in front of mine at their current educational level.
Teaching Applied Mathematics
I had the privilege to teach and work closely with both graduate and undergraduate students at an early stage of my academic career from 2004 to 2010, in the fields of mathematics and engineering. During this time, I have participated as a teaching assistant in several courses including:
- Applied Mathematics.
- Differential equations 1
- Differential equations 2
- Linear algebra.
- Advanced Linear algebra.
- Matlab programming
- Numerical analysis
- Partial differential equation.
- Pure Mathematics.
- Advanced Mathematical Methods.
- Engineering Mathematics.
These courses were common among different majors mainly, physics, mathematics and various fields of engineering. Therefore, The variety of the courses I taught provided me with a unique opportunity to be exposed to multidisciplinary areas and make connections between the different fields of science and engineering. This diversity allowed me to bring different points of view to the classroom to enrich the students’ experience, account for the different backgrounds and develop their analytical thinking skills. Moreover, the size of the classes I taught varied from small classes (20 students) to large classes (500 students). This variation allowed me to learn how to manage a large group of students by engaging them by asking challenging questions and giving practical examples periodically during the class.
I believe that motivation and engagement are the key elements in the learning process. Therefore my main strategy is motivating students for the subject as well as engaging them in the teaching activities. Using motivational strategies such as discovering a pattern, the usefulness of a topic, presenting a reasonable challenge, helped me maintain the student?s excitement and engagement. Furthermore, I have succeeded in changing students' attitudes towards mathematics and how useful to learn it and its applications in real life. The feedback from my students and colleagues was a clear indication that my strategy succeeded as indicated at the end of this statement.
Teaching Electrical Engineering
In 2010, I moved to Australia to start my Ph.D. in the field of electrical engineering; in particular, dynamical systems and control. This allowed me to get involved more in teaching practical engineering subjects. Since electrical engineering is one of the branches that heavily uses mathematics and modeling; I was able to use my knowledge in pure and applied mathematics in the classes I taught. Moreover, engineering added a practical flavor and a realistic touch to the way I teach. For instance, I used to teach Laplace and Fourier transforms as a purely mathematical transformation. However, teaching these subjects form an engineering perspective enriched my knowledge with the practical side of the abstract concepts.
My first feedback from engineering students was outstanding. One student wrote the following statement on my evaluation form, “You are the best teacher and tutor we ever had”. This sentence paid off all my efforts in teaching and gave me a glimpse that I am on the right track.
Later, during my post-doctoral studies at the school of Engineering and Information Technology at UNSW, I shared teaching load and designing the syllabus of different engineering courses including:
- Introduction to Electrical Engineering,
- Vibration and Control,
- Design of Electronic Circuits 1,
- Design of Electronic Circuits 3.
Teaching design engineering courses allowed me to apply mathematics to complex real-world problems. It made me realize Leonardo da Vincishs quote, “Mechanics is the paradise of the mathematical sciences because by means of it one comes to the fruits of mathematics”.
In addition to that, I was privileged to participate in many professional training courses to enhance my coaching and teaching skills. These trainings were conducted by professional trainers and experts to help us develop our teaching skills. These courses include:
- Graduate Teaching Training Program (GTTP). University of New South Wales Canberra, Australia.
- Training of Trainers course (TOT) from the Institute of Development and Learning, Elmansora University, EGYPT.
- Teacher Training Course from Institute of Development and Learning, Suez Canal University, Ismailia, EGYPT.Moreover, I have a skills assessment as a university tutor from Australia’s leading vocational education and training assessment provider (VETASSESS).
Furthermore, I participated in the All Unit at UNSW Canberra to help students with learning difficulties in related topics. I received the following feedback forms from my previous coordinator in UNSW which exhibits positive feedback about my teaching and coaching style; “After speaking to my coordinator, he particularly liked that I begin teaching by assuming students having no maths background at all and between you figured out where he was up to“.
Online coaching and teaching
Being passionate about teaching and coaching was the main motive for me to be a co-founder of a scientific online platform named Egyptscholars. That is an independent, non-profit organization founded on the principle of volunteerism registered in California, USA.
Currently, I am acting as a lead team member of the Egyptscholars labs team, which provides a platform where the students can learn, discuss ideas, implement them, and get evaluated. This is done with an online environment where a group of candidates gets mentoring and practical experience in scientific research and other disciplines through a group of academic and industry-related mentors. I have been one of the core teams in Egyptscholars labs for the last three years. Also, I was part of the editorial board two books produced by Egyptscholars about basic scientific research and guide to study abroad.
I have also conducted several online webinars on topics related to my area of expertise. So far, some of these lectures are online, and feedback from students has been very positive.
Courses that suit my interests and background
The following is a list of courses that suit my interests and background:
- All the basic undergraduate pure and applied mathematics courses: These includes courses like Single Variable Calculus; Multivariable Calculus; Differential Equations; Linear Algebra; Real Analysis; Numerical Analysis; ect…
- Signals and Systems: This course will introduce fundamental concepts from signals and systems modeling and analysis. Topics will include the sampling theorem, the Fourier transform of continuous and discrete-time signals, ¯lter design and introduction to the statespace framework.
- Engineering mathematical analysis: This course introduced fundamentals of linear algebra, real and complex analysis, differential equations, random processes and introduction to optimization and search methods.
- Analytical Dynamics: This course focuses on the development of the Lagrangian and Hamiltonian formulation of dynamical systems. The course will emphasize the use of energy-based principles to model complex dynamical systems.
- Linear Systems Theory: This course covers the fundamental concepts of vector spaces and linear operators at the graduate level. Topics will include system-theoretic principles such controllability, observability, linear quadratic optimization and the linear quadratic Gaussian (LQG) framework.
- Nonlinear Systems and Controls: The course introduces nonlinear phenomena arising in physics and engineering. Topics will include Lyapunov stability analysis, the input-output approach to stability, the absolute stability problem and its formulation using recent tools from semi-definite programming (SDP), rigorous treatment of nonlinear control methods such as feedback linearization, sliding mode, adaptive techniques, and passivity-based methods.
Robust Control Theory: This course will unify system-theoretic tools and optimization-based techniques for multi-input-multi-output systems. The course will address model uncertainty quantification, stability/synthesis using small-gain and dissipativity theorems applied to the and frameworks. The course will emphasize the role of convexity in the problem formulation and solution using tools from SDP.
- Optimal Control: This course will be based on the calculus of variations, the minimum principle, and dynamic programming. The course will address modern numerical solution techniques to optimal control problems derived from nonlinear programming. The course will include applications from model predictive control and hybrid systems.
- Discrete mathematics: This course covers elementary discrete mathematics for computer science and engineering. It emphasizes mathematical definitions and proofs as well as applicable methods. Topics include formal logic notation, proof methods; induction, well-ordering; sets, relations; elementary graph theory; integer congruences; asymptotic notation and growth of functions; permutations and combinations, counting principles; discrete probability.