# Mathematical Structures For Computer Science : ... [Extra Quality]

Authors Judith L. GerstingJudith Gersting received her undergraduate degree in mathematics from Stetson University. Her master's and Ph.D. in mathematics are from Arizona State University. She taught mathematics and, later, computer science at Indiana University-Purdue University at Indianapolis, where she was the first chair of the newly formed Computer and Information Science Department. She was a Staff Scientist at the Indianapolis Center for Advanced Research for two years, and also spent a year as the Assistant Chair of the Department of Computer Science at the University of Central Florida. After many years at IUPUI, she and her husband, John Gersting, left IUPUI to go to the Computer Science and Engineering Department at the University of Hawaii at Hilo on the Big Island. Here Prof. Gersting served as department chair for many more years, and was awarded the University of Hawaii Regents Medal for Excellence in Teaching. She and her husband have recently retired from UHH and are back as Adjunct Professors at IUPUI teaching two classes per semester. Prof. Gersting has been active in SIGCSE (the ACM Special Interest Group in Computer Science Education), and she was the co-chair of the SIGCSE Technical Symposium in 2002. She has received NSF computer science education grants and has served on NSF grant review panels in computer science education. She is the author of several college-level textbooks in mathematics and computer science, including co-author with G. Michael Schneider of the introductory text Invitation to Computer Science, published by Cengage Learning.

## Mathematical structures for computer science : ...

Judith L. GerstingJudith Gersting received her undergraduate degree in mathematics from Stetson University. Her master's and Ph.D. in mathematics are from Arizona State University. She taught mathematics and, later, computer science at Indiana University-Purdue University at Indianapolis, where she was the first chair of the newly formed Computer and Information Science Department. She was a Staff Scientist at the Indianapolis Center for Advanced Research for two years, and also spent a year as the Assistant Chair of the Department of Computer Science at the University of Central Florida. After many years at IUPUI, she and her husband, John Gersting, left IUPUI to go to the Computer Science and Engineering Department at the University of Hawaii at Hilo on the Big Island. Here Prof. Gersting served as department chair for many more years, and was awarded the University of Hawaii Regents Medal for Excellence in Teaching. She and her husband have recently retired from UHH and are back as Adjunct Professors at IUPUI teaching two classes per semester. Prof. Gersting has been active in SIGCSE (the ACM Special Interest Group in Computer Science Education), and she was the co-chair of the SIGCSE Technical Symposium in 2002. She has received NSF computer science education grants and has served on NSF grant review panels in computer science education. She is the author of several college-level textbooks in mathematics and computer science, including co-author with G. Michael Schneider of the introductory text Invitation to Computer Science, published by Cengage Learning.

Mathematical Structures in Computer Science is a journal of theoretical computer science which focuses on the application of ideas from the structural side of mathematics and mathematical logic to computer science. The journal aims to bridge the gap between theoretical contributions and software design, publishing original papers of a high standard and broad surveys with original perspectives in all areas of computing, provided that ideas or results from logic, algebra, geometry, category theory or other areas of logic and mathematics form a basis for the work. The journal welcomes applications to computing based on the use of specific mathematical structures (e.g. topological and order-theoretic structures) as well as on proof-theoretic notions or results.

The students will improve their knowledge of the algebraic structures that are most often employed in informatics. These will be mathematical logic, algebra, functional alalysis and graph theory. This will enable them to better understand the theoretical foundations of informatics and also conduct research work in the field.

The aim of the subject is to improve the students' knowlende of the basic mathematical structures that are often utilized in different branches of informatics. In addition to universal algebra and the classical algebraic structures, foundations will be discussed of the mathematical logic, the theory of Banach and Hilbert spaces, and the theory of both udirected and directed graphs.

CS 0441 Discrete Structures for Computer Science is a mathematics course which focuses on the study of mathematical structures that are discrete rather than continuous. This means that the objects within the mathematical structures that you'll learn about are distincly separated values. This course will focus heavily on the integers (which are discrete by nature), whereas a continuous field like calculus focuses more on real numbers. Lets start with a birds-eye view of the main topics covered in 441:

4 hours. A discrete mathematics course where concepts of discrete structures will be applied to computer science. Topics include elementary set theory, logic, functions, relations, Boolean algebra, elements of graph theory, matrix representation of graphs, and matrix manipulations, mathematical induction, counting techniques and discrete probability theory. Prerequisites: CSC 211; MTH 123 or MTH 125 or MTH 130 or MTH 230 or MTH 231 or MTH 235

Mathematics plays a key role in computer science, some researchers would consider computers as nothing but the physical embodiment of mathematical systems. And whether you are designing a digital circuit, a computer program or a new programming language, you need mathematics to be able to reason about the design -- its correctness, robustness and dependability. This book covers the foundational mathematics necessary for courses in computer science.

The common approach to presenting mathematical concepts and operators is to define them in terms of properties they satisfy, and then based on these definitions develop ways of computing the result of applying the operators and prove them correct. This book is mainly written for computer science students, so here the author takes a different approach: he starts by defining ways of calculating the results of applying the operators and then proves that they satisfy various properties. After justifying his underlying approach the author offers detailed chapters covering propositional logic, predicate calculus, sets, relations, discrete structures, structured types, numbers, and reasoning about programs.

"Profound knowledge and skills in discrete mathematics are mandatory for a well educated computer scientist. Therefore a corresponding curriculum typically requires at least a basic course on this subject. This textbook, which is based on the lectures given by the author at the University of Malta, is a perfect companion for every student taking such a course. ... Besides a thorough formal presentation the book always gives a convincing motivation for studying the corresponding structures and explains the main ideas using illustrations. A well chosen set of exercises rounds off each topic. After studying the presented material a computer science student will be well prepared for further, more specialized courses." [Martin Leucker, Lübeck]

4 hours. A discrete mathematics course where concepts of discrete structures will be applied to computer science. Topics include elementary set theory, logic, functions, relations, Boolean algebra, elements of graph theory, matrix representation of graphs, matrix manipulations, mathematical induction, counting techniques and discrete probability theory. Prerequisites: CSC 211 with a grade of C or higher; MTH 123 or MTH 125 or MTH 130 or MTH 230 or MTH 231 or MTH 235.

Unlike science, which investigates the natural world, or political science, which analyzes the institutions we have been using for thousands of years, computer science is newer, more nuanced, and often much more challenging to absorb.

Computer science can be intimidating, but it can be done. Becoming a proficient computer scientist does, however, require an intermediate or advanced understanding of a couple of subjects, including math.

It is important to note that not all computer scientists use math every day. In fact, some never use it at all. But math is still useful for two reasons. First, many computer scientists do use math every day, making the subject nothing less than a requirement for certain jobs. Second, math can help us to develop the underlying logic that working in computer science requires.

As a complicated field, there are various types of math in computer science. Computer science examines the principles and use of computers in processing information, designing hardware and software, and using applications. Possessing a strong foundational knowledge of mathematics is vital to gaining an understanding of how computers work. Mathematics is a fundamental scholarly tool in computing.

In our industrialized world, we deal with resources and conversions between resources on a daily basis. For example, one can consider collections of chemical molecules as resources, and chemical reactions like 2H_2 + O_2 --> 2 H_2O as conversions between these. In this talk, I will introduce the mathematical definition of what constitutes a theory of resource convertibility, and illustrate which kinds of theorems can be proved in complete generality. There are also some lessons to be learnt on the rôle that ordered structures play in algebra. 041b061a72