Mathematicians often speak informally about how one definition of an object is preferable to other equivalent choices, about how one proof of a mathematical theorem is more transparent or constructive than alternatives, or about the “complexity” of an object guaranteed to exist by a theorem (i.e. can we actually “find it” or somehow get our hands on it). Turning these somewhat philosophical and...

This paper studies a formal mathematical description and the block diagram of the secret system and, by analogy with the theory of secret systems, introduces the basic elements and mathematical operators, abstractly d escribing steganographic informat ion protection system.

Tolerance is essential for integration of CAD and CAM. Unfortunately, the meaning of tolerances in the national standard is expressed in graphical and language forms and is not adaptable for expression, processing and data transferring with computers. How to interpret its semantics is becoming a focus of relevant studies. This work based on the mathematical definition of form tolerance in ANSI ...

A p-hub center network design problem is definition of some nodes as hubs and allocation of non-hub nodes to them wherein the maximum travel times between any pair of nodes is minimized. The distinctive feature of this study is proposing a new mathematical formulation for modeling costs in a p-hub center problem. Here, instead of considering costs as a linear function of distance, for the first...

This paper starts by discussing Nelson’s philosophy of mathematics, which is a blend of mathematical formalism and a radical constructivism. As such, it makes strong assertions about the foundations of mathematic and the reality of mathematical objects. We then offer our own suggestions for the definition of mathematics and the nature of mathematical reality. We suggest a second characterizatio...

This paper describes CAMA (Computer-Aided Mathematical Analysis), which is a system that attempts to handle all conceivable mathematical operations, from simple numeric procedures to complex algebraic or settheoretic manipulations. CAMA operates in a timesharing environment with a large central computer and a remote terminal computer with graphical devices. Some of the features of CAMA are: the...

Now, we will begin the proving of some theorems, a skill which you will need in the upper division courses for which Math 111 is a prerequisite. For clarity, we will define theorem, proof, and definition. A theorem is a mathematical statement that is true and can be (and has been) verified as true. A proof of a theorem is a written verification that shows that the theorem is true. A definition ...