Two philosophical ideas motivate this paper. The first is an answer to the question of what is an appropriate activity for a physicist. My answer is that an appropriate activity is anything where the tools of a physicist enable him or her to make a contribution to the solution of a significant problem. This may be obvious in areas that overlap…

The method of proof by mathematical induction follows from Peano axiom 5. We give three properties which are often used in the proofs by mathematical induction. We show that these are equivalent. Supposing the well-ordering property we prove the validity of this method without using Peano axiom 5. Finally, we introduce the simplest form of…

In teaching primary teacher trainees, an awareness of the characteristic features, especially commutativity and associativity of basic operations play an important role. Owing to a deeply set automatism rooted in their primary and secondary education, teacher trainees think that such characteristics of addition are so trivial that they do not need…

The presentation of physics content knowledge in conjunction with the lack of examples in solving problems leads high school students to struggle with mathematical problem solving in physics courses. This paper explains the importance and necessity of having mathematical courses for all high school students. (YDS)

Application of quadratic equations to standard problem in chemistry like finding equilibrium concentrations of ions in an acid solution is explained. This clearly shows that pure mathematical analysis has meaningful applications in other areas as well.

Derives the general Doppler formula in a nonstatic universe using assumptions of special relativity, homogeneity and isotropy of the universe. Examples of applications to physical cosmology are given. (SL)

Presents a mathematical game called the dinner-guest problem that deals with Steiner triple systems. (HM)

By providing an example problem in solving sets of nonlinear algebraic equations, the advantages and disadvantages of two methods for its solution, the tearing approach v the Newton-Raphson approach, are elucidated. (CS)

Considered are the main elements of computational chemistry problems and how these elements can be used to formulate the problems mathematically. Techniques that are useful in devising an appropriate solution are also considered. (Author/TG)

Definitions of estimating and approximating are given and areas where these skills are used (such as practical situations, problem solving, and measurement) are discussed. Nine activities which range from second to twelfth-grade level are suggested. (MK)

Back-of-the-envelope problems call for approximate calculations of quantities that can be related to information in a person's knowledge but are not solved precisely. These problems provide an opportunity for the study of processes and the role of general knowledge in ill-defined problem solving. Subjects with advanced and intermediate knowledge…

Develops a graphical method for studying the parallel susceptibility of an antiferromagnetic material. (SL)

Describes the numerical methods of relaxation and over-relaxation for solving Laplace's equation for a system of conductors, and gives several examples of their use. (Author/GA)

Gives a sketch of some topics in distribution theory that is technically simple, yet provides techniques for handling the partial differential equations satisfied by the most important Green's functions in physics. (Author/GA)

Provides six short story problems that are solved using common physics concepts. Includes solutions. (MVL)