"The flair Furniture Company produces inexpensive tables and chairs. The production process for each is similar in that both requires a certain number of hours of carpentry work and a certain... More > number of labor hours in the painting and varnishing department. Each table takes 4 hours of carpentry and 2 hours in painting and varnishing shop. Each chair requires 3 hours in carpentry and 1 hour in painting and varnishing. During the current production period 240 hours of carpentry time and 100 hours in painting and varnishing time are available. Each table sold yields a profit of $7; each chair produced is sold for a $5 profit.
Design a Linear programming problem for the flair Furniture Company and find the combination of tables and chairs that the company must produce to maximize profits.
"< Less

In a study of housing demand, the county assessor is interested in developing a regression model to estimate the market value (i.e., selling price) of residential property within her jurisdiction. In... More > addition, the assessor feels that there may be other important variables that will affect the market value of the house such as the size of the house, number of rooms, age and whether the house has an attached garage. These data for 15 randomly selected houses arc shown in the attached table.< Less

This book fills a gap in the linear programming literature, by explaining the steps that are illustrated but not always fully explained in every elementary operations book — the steps that lead... More > from the elementary and intuitive graphical method of solution to the more advanced simplex tableau method.
Most of the world, even those technically trained, can get along very well by seeing a few illustrations of simple linear programming problems solved graphically, followed by instruction in the use of computer software for solving real-world problems. But there needs to be a coterie of initiates who understand the process well enough to explain it to others, to know what the pitfalls, ramifications and special cases are, and to provide further developments. I have used an informal narrative style with a number of worked out examples and detailed explanations, to put the topic within reach.< Less

This book fills a gap in the linear programming literature, by explaining the steps that are illustrated but not always fully explained in every elementary operations book — the steps that lead... More > from the elementary and intuitive graphical method of solution to the more advanced simplex tableau method.
Most of the world, even those technically trained, can get along very well by seeing a few illustrations of simple linear programming problems solved graphically, followed by instruction in the use of computer software for solving real-world problems. But there needs to be a coterie of initiates who understand the process well enough to explain it to others, to know what the pitfalls, ramifications and special cases are, and to provide further developments. I have used an informal narrative style with a number of worked out examples and detailed explanations, to put the topic within reach.< Less

It is a first linear algebra course for mathematically advanced students. It is intended for a student who, while not yet very familiar with abstract reasoning, is willing to study more rigorous... More > mathematics that is presented in a "cookbook style" calculus type course. It is also supposed to be a first course introducing a student to rigorous proof and formal definitions.
The target audience explains the specific blend of elementary ideas and concrete examples, which are usually presented in introductory linear algebra texts with more abstract definitions and constructions typical for advanced books.
The book emphasizes topics that are important for analysis, geometry, probability, etc., and does not include some traditional topics. For example, I am only considering vector spaces over the fields of real or complex numbers, since I feel time would be better spent on some more classical topics, which will be required in other disciplines.< Less

A box manufacturing plant makes two types of boxes, each of which requires time on the saw for cutting, then time on the assembly and later for finishing. Suppose Model A requires 1 hour cutting, 2... More > hours of assembly and 1 hour of finishing. Model B requires 1 hour of cutting, 1 hour of assembly and 3 hours of finishing. There are 40 man hours available for cutting per week, 60 man hours for assembly and 90 man hours for finishing. Suppose each model A box sold brings in $20 profit and each model B box sold brings in $25 profit. Determine the number of each box that should be produced to maximize the profit.< Less

The 20th century saw a large number of results regarding the Zero-multiplicity of rational linear recurrence sequences; those are the number of times zero is found in a particular recurrence... More > sequence. Of particular interest is the result of Skolem-Mahler-Lech and the result of F. Beukers. Respectively these results are: for every linear recurrence sequence the zeroes are a finite set along with a finite number of arithmetic sequences, and, with the exception of a special subset, every ternary linear recurrence sequence has a multiplicity less than seven. Both of these results rely heavily on p-adic techniques and the behavior of algebraic numbers within the p-adic numbers.< Less

The 20th century saw a large number of results regarding the Zero-multiplicity of rational linear recurrence sequences; those are the number of times zero is found in a particular recurrence... More > sequence. Of particular interest is the result of Skolem-Mahler-Lech and the result of F. Beukers. Respectively these results are: for every linear recurrence sequence the zeroes are a finite set along with a finite number of arithmetic sequences, and, with the exception of a special subset, every ternary linear recurrence sequence has a multiplicity less than seven. Both of these results rely heavily on p-adic techniques and the behavior of algebraic numbers within the p-adic numbers.< Less

Explore the future of a mankind where a large number of planets and moons are now colonized. Time Travelers, such as your character, explore the past to record history and prevent Renegade time... More > travelers from changing time.< Less

This essay describes a way of finding hypercomplex numbers—ones that extend complex numbers to more dimensions—with only basic algebra plus Ayn Rand’s philosophy, Objectivism. The... More > result has implications for mathematics and the philosophy of science. The “RADN numbers” (known by science under another name) have a property of rotation like complex numbers, and are also commutative/distributive. (Division is deemed less crucial.) The author of UITHN asked himself what exactly numbers are, how they arise in our mind, and what their relation to reality is. But these questions were so fruitful only because he used a correct philosophy. Another philosophy, such as Karl Popper’s, would not have worked. This has two implications: Rand’s philosophy has epistemological truth; and the RADN numbers may have unique significance. May spur thought on mathematics, addition, multiplication, dimensions, imaginary units, and dimensioned numbers, and lead to more appreciation of Rand’s ideas.< Less