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 http://science.kennesaw.edu/~mburke/modules

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. http://www.csc.ncsu.edu/faculty/ref/why.na.html 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:
http://www2.ncsu.edu/eos/info/math/ma132_info/ma132hp.htm
http://www2.ncsu.edu/eos/info/math/ma302_info/white/ma302hp.htm
http://www2.ncsu.edu/eos/info/math/ma402_info/402hp.htm ">