Difficulties in Calculating

Thomas Rosen’s Discrete Mathematics and Its Applications offers a detailed, accessible, thorough approach to discrete mathematics. This world-famous best-seller was written for students in a number of mathematics departments and majors, including applied mathematics, engineering, and computer science. It was originally written as a book for advanced mathematics undergraduates. But with its wide appeal and Rosen’s many comments on various topics, it has become a valuable text for graduate students in all mathematics departments.

 

The key features of Discrete Mathematics are its accessibility, its simplicity, its elegance, its directness, its affordability, its depth, its interpretability, and its usefulness to a wide range of students. Its main contributions to discrete mathematics are its powerful analysis and application to all areas of mathematics. This includes application to problems in algebra, number theory, geometry, calculus, and other fields. In fact, the subject matter is so broad that the reader will find many topics not covered by Rosen in this text.

 

A strong part of the book is its introduction to number theory and discrete mathematics. The author rightly points out that many students’ initial experiences with number theory are limited and they may find it difficult to relate discrete mathematics to real life situations. For instance, if a student has learned about discrete math from a text or from another teacher, he or she might be unable to relate elliptical curves to security systems and might have difficulty finding discrete mathematics equivalent to quantum mechanics. But from the very first chapter of this text, Rosen makes it clear that this is not the case. Security systems based on elliptical curves are well studied throughout the text.

 

In addition, as suggested in the introduction to the book, there are many nontrivial applications of discrete mathematics and even some applications which are seemingly nontrivial but which in fact are necessary for numerical reasoning. Examples include discrete optimization and certain types of probability. These examples allow the student to learn about various nontrivial applications and then apply them to real world problems.

 

In order to truly understand and learn discrete mathematics, it is important to be able to analyze various pieces of data without having to rely upon any outside source. This is exactly what happens in the examples given in this text. The student is presented with a series of graphs, each depicting a discrete mathematical problem, and then he or she has to analyze the data without having to rely upon any outside information. Indeed, many of the examples in the text even show the student manually analyzing a set of discrete graphs.

 

Of course, not all sets of numbers can be considered discrete. This is why the author uses the infinite alphabet to represent the real numbers. Here are two examples from the text that demonstrate the importance of the finite alphabet when working with discrete mathematics. The first example is of course the Fibonacci calculator, which as we all know, is an infinite alphabet that cannot contain countable elements.

 

The second example comes from the field of computer science and its application to discrete mathematics and its first cousin, graph theory. In this case, we are talking about the algorithms of digital computers. This is the field that uses computer science to solve some of the more complicated algorithms such as the sorting algorithm. It is also used in the search engines, for instance Google and other large search companies.

 

In conclusion, it’s clear that a lot of thought has gone into topics such as elliptical calculus, infinite algebra, and graph theory. And while many of these subjects look simple at first, they can have a number of complexities that become very tough to handle for the average person. So, don’t think that a master’s degree in discrete mathematics is unnecessary for someone who works in an area that is considered relatively simple and easy to grasp. Rather, take the time to learn the various discrete objects so you can work them out yourself and save yourself a lot of time and money in the future.