E. Kengne on Google Scholar; MathSciNet; Research Gate; ZentralBlatt; mathnet.ru; genealogy.ams; Academic Search; with MR Citation; Academic Search; Yahoo-search (Mathematics); Excite-search
believe that my philosophy of teaching is relatively simple. I base my
teaching on the belief that the simple way to learn mathematics is to
do mathematics. While the process of reading examples and proofs in
textbooks and from lecture notes is valuable, the real learning comes
through one's own efforts at solving mathematical problems, either
computational, theoretical, or both. This is achieved mostly through
class assignments, but also through in-class discussions and exercises.
I view my role as a facilitator for this process. I must design the
framework in which learning can take place, and then stimulate and
nurture the students' development, giving help in terms of knowledge,
techniques, and encouragement.
I do my best to help the students learn to think logically, learn
problem-solving methods and techniques, and improve writing skills
(writing clearly and concisely, explaining step-by-step processes,
providing valid reasons for logical arguments). In addition, I try to
help students see the course material in a holistic context by
requiring them to synthesize the various concepts of the course by
applying them together.
I have taught a wide variety of courses for a wide variety of students.
For mathematicians: mathematical analysis, real analysis sequence,
functional series, integral and differential calculus, ordinary
differential equations, partial differential equations, analytical
geometry, linear programming, optimization, integral transforms,
numerical analysis; For physicists and For engineers: special functions
of the mathematical physics, equations of the mathematical physics,
Fourier series, Fourier and Laplace transforms, engineering Calculus
sequence, mathematics for engineering; For computer scientists:
scientific calculus and programming, linear programming and discrete
optimization, mathematics for computer sciences, numerical calculus;
For life sciences: calculus for life sciences.
The purpose of grading is mostly motivational than judgmental. By
requiring students to demonstrate knowledge of course material, this
motivates them to do the necessary work required to learn mathematics.
I always grade on a flexible curve. I usually curve each exam and also
the total assignment scores and quiz scores. The curve is based on a
mixture of class performance, percentage correct, and comparison with
past classes' performances on the same material. Thus, it is possible
for everyone in the class to get a good grade, or the opposite. It is
rare for a student who attends class regularly and does all of the
class work to receive a grade below a C. On the other hand, to receive
an A, one must score consistently high marks on exams.
generally spend quite a lot of time in the process of grading by taking
one exercise, marking it for all students before to pass to the next
question. This method allows me to be more equitable for all
In order to increase communication and feedback both to and from my
students, I encourage the use of office hours, and I make myself
available at other hours as well. I have a Web page which allows
students access to all sorts of class information and which also
includes a feedback form for students to submit suggestions and
comments. I generally use the email of my students to notify them of
changes or hints on assignments, temporary changes in office hours, etc.
I always hold many office hours per week, and I make myself available
at other times as well. I tell my students they are welcome to come by
my office at other times, and unless I have an immediate deadline or
meeting or class, I will be able to help them. My detailed schedule is
posted on my Web homepage.
Class sessions - lecture and discussion:
I always begin each class with a brief summary of the previous class
session, and a reminder of where we are in the topic we are currently
working on. At this point I usually ask if there are any questions from
the reading, homework, or previous class. After this discussion, I
usually give a lecture on new material. I try to begin the lecture with
a brief outline and a list of objectives, and I try to always include
examples during the lecture.
I try to present course material in analytical, numerical, and
graphical contexts. While this approach of course depends on the
particular topic, it is particularly valuable in calculus, differential
equations, and numerical analysis courses. I am especially conscious of
using figures to help illustrate different concepts, as most students
can then at least intuitively understand the concepts even if they have
trouble understanding the analysis.
Technique of learning:
In the past several years, I have incorporated more cooperative
learning techniques into the class sessions. These techniques usually
involve working in pairs or groups of three on a short problem, with
specific instructions on how to share ideas and come up with a common
solution. While the groups are working, I can move around the classroom
to help various groups, and at the end we compare and discuss the
various groups' solutions.
Homework and level of difficulty:
Knowing that the only way to learn mathematics is to do mathematics, I
usually assign a lot of homework. I try to assign a mixture of routine
and challenging problems so that I can stimulate the more advanced
students but still enable the poorer students to at least learn the
basics of the course material. Usually, I try to grade as much of the
homework as possible. For large classes, students can check their work
on routine assignments by using solutions manuals, the help room, and
posted solutions, and by asking questions in class.
When I create an exam, I try to follow several guidelines. First, I try
to test over a reasonable range of class material, and I try to stress
the important concepts. I also include problems of varying difficulty.
However, I usually do not include trivial problems. Before each exam, I
spend some time in class discussing what topics will be covered and
which are most important. I usually give more detail for undergraduate
courses, especially the lower level courses; I sometimes give them the
so-called exam model. I also try to be careful not to make the exams
too long, but I sometimes fail in this regard. I find this is
especially hard in higher level theory courses, where it is very hard
to judge how long it will take students to do the creative thinking
necessary to come up with a correct proof. Consequently, in these
courses I do not expect students to solve all of the problems on the
Course Syllabi and Information
At the first class meeting, I hand out a syllabus which gives the basic
information for the course. It lists ways to contact me: office number,
phone number, and email address, and also the address of my Web
homepage and the homepage for the class. It also informs the students
about the prerequisites, text, topics to be covered, the number of
exams and quizzes, information on homework, and grading policy. If the
class requires use of a calculator and/or computer, the syllabus
includes a section describing how they will be used in the class and
what will be expected from the students in the areas of programming and
calculator/computer expertise. Finally, the syllabus also includes a
section on use of the class Web page.
During the first week I remember my office hours (also listed on my Web
homepage, along with my more detailed schedule). I do not give out a
list of all homework assignments for the semester as some instructors
do. I prefer the flexibility of changing the problems and due dates
during the semester as I get to know the strengths and weaknesses of
the students. This allows me to tailor the assignments to the needs of