Opportunities arise in lower level mathematics courses to present
certain types of numerical methods. The authors will illustrate how
topics such as Newton's Method, error analysis in Taylor series, and
the method of Least Squares can be included in calculus courses.
In addition, the introduction of numerical methods in undergraduate
differential equations courses will be discussed.
This talk will describe a project whose objective is to develop a library of mathematical modules which address applications in the undergraduate biology and chemistry curricula. Each module centers upon a specific application chosen from the biology or chemistry curriculum and has different parts which address that same application at the levels of precalculus, differential calculus, integral calculus, and differential equations. The modules can serve as material for group project assignments in these math courses and can also be used in the relevant science courses to enhance the study of theory and/or the carrying out of lab experiments.
Through repeated visits to the same applications, but equipped with more mathematical power at each visit, students will gain an understanding of the process of how increasingly demanding questions about the applications necessitate the development of more sophisticated mathematical tools to help answer those questions.
The modules produced are stored on our World Wide Web Site
This special session of the Teaching Issues is designed for colleagues
to share their experiences and to discuss issues in teaching numerical
analysis, numerical methods or scientific computing at
the undergraduate level. As the organizer of this special session, I
will first give a list of issues arising in the teaching of numerical
analysis, numerical methods or scientific computing at the
undergraduate level. Some of the issues, like curriculum reform, choices
of textbooks, uses of technology in teaching, uses of applications and
real-world problems in teaching and so on, will be addressed by speakers
of this session and all issues are open for discussion during the session
after talks. I then will share my experiences in teaching numerical
methods I and II at the Citadel. Mainly, I will discuss: curriculum
change (from numerical analysis to numerical methods); and the
uses of MatLab as a teaching tool and a programming language for
students to implement algorithms and to solve problems.
Floating point computing is an essential part of the core of computer
science that a graduate must know, cf.
The multitudeness set of numerical analysis topics contains important
efficacious subsets for the computer science major; e.g.,
IEEE floating point standard (WK Turing Award); conditioning of
problems and stability of algorithms including backward error analysis
(JW Turing Award), complexity and other comparisons of algorithms
(good paradigm problem is f(x)=0), use of numerical software libraries,
etc. My view on the content of such a necessary course will be outlined.
This talk will examine some current and classical numerical analysis
texts in an attempt to gain an understanding of the history of the field.
The review should be helpful in determining current trends
and their implications for the teaching of numerical analysis.
Theorems on a hierarchy of generalized inverses of a matrix that include
equation-solving, reflexive, minimum-norm, least-square inverses and
the pseudoinverse are discussed,in a form accessible to undergraduates,
along with the support of a collection of MATLAB exercises to
compute this hierarchy of inverses,adapting the MATLAB rref command to
construct a Hermite normal form.These exercises are designed to
illustrate and unify the concepts of rank, fundamental
subspaces and projections onto these subspaces,and are appropriate for a
junior/senior course on (numerical)linear algebra or a first year
graduate course on linear algebra.
Coastal Carolina University is a four year liberal arts university
offering undergraduate degrees in several fields. Students enrolled
in the mathematics program get a bachelors degree in Applied
Mathematics. Most of the students taking the numerical analysis class
are double majors is computer science or marine science. In this
talk I will present the different ways I tried to teach
this class for the past seven years. Issues that will be discussed are:
textbooks adopted, programming language used, the operating system
platform, balancing the coverage of theory and
applications and students attitudes towards this class.
Two computational mathematics one credit courses, and a three credit
course will be described. All three courses are application driven
and have components of mathematics and computations.
A one credit course (ma132) for the life and management science
students, who have passed one semester of calculus, uses the
Excel spreadsheet. Applications to data fitting, time dependent
models and optimization are stressed. The one credit course (ma302) for
the physical science and engineering students, who have passed
two semesters of calculus, uses Matlab. Traditional
applications to mechanics, circuits and population models are stressed.
The three credit course (ma402) introduces the student numerical
solution of partial differential equations, stresses heat
and mass transfer applications, uses Matlab and high performance
computing. Complete documentation can be found at: