2000 Solved Problems In Discrete Mathematics Pdf


2000 Solved Problems In Discrete Mathematics Pdf

we use the collection of axioms, definitions, and theorems in a mathematical system to prove theorems about that system. a mathematical proof is one in which theorems are proved by using mathematical arguments. a proof must be logically sound. to be logically sound, a proof must be completely self-consistent. it must follow the rules of the logic and mathematics. proofs must be logically valid. they are the intellectual effort to convince someone else of something that you know to be true.

we will examine the use of the concept of graph theory in the search for theorems in discrete mathematics. we will approach this topic from the point of view of the students as well as that of the teacher. we will formulate the problem that the teacher can present to the students, and propose a way to present the problem to the students. we will show some examples of the graphs that we can use as a model for the problem, and we will draw several examples of theorems that can be obtained through the use of the graph model. we will discuss the role of the students during the construction of the graph and the understanding of a mathematical problem.

in this book, we will present the latest advances in areas that are essential to mathematics education. there are many areas that constitute a very important part of mathematics and, in the last years, have been the object of research. some of these areas are areas of logic, proof theory, model theory and automata theory, others are areas of numbers, graph theory and combinatorics.

we will use a computer to solve a number of mathematical problems. the problems are taken from the book by benoit, c. and lautemann, s. (2017). we will study the procedures that are used to solve the problems, in particular, we will study which parts of the problem are solved by the computer, and we will describe the motivation for the choice of the problems.

the high-school mathematics curriculum is still evolving in many countries. although students are expected to take the first two years of high school mathematics, as well as algebra i, most countries do not require students to take a discrete mathematics course in the second year. but with the new common core standards in math and science, the second year of high school mathematics is increasingly required to include discrete mathematics. similarly, in australia, high school mathematics consists of the first two years of algebra i and geometry and a third year of linear algebra and discrete mathematics.
the main goal of the project is to investigate whether and to what extent the knowledge base of young students influences their performance in the last part of the first year of the bachelor degree in mathematics. an important aspect of the research is the analysis of the data which is collected in terms of the different topics. the analysis is done by a statistical approach, in particular by means of regression models. this requires a series of actions that must be carried out in different steps. the final objective is to identify the different variables that influence the student’s performance in mathematics during the last year of their undergraduate studies.
expected outcomes: the expected outcomes of the research project are mainly: (a) to develop a well-structured curriculum for discrete mathematics in the first two years of the bachelor degree in mathematics, (b) to evaluate the impact of such curriculum on the students’ performance in the last year of their degree (c) to develop and evaluate a computer-based assessment system for the assessment of students’ competence in discrete mathematics. the assessment system should be based on a series of real-world problems, suitably structured and designed by experts, and on a battery of computer-based assessment tests that cover the concepts of discrete mathematics taught during the first two years of a bachelor’s degree in mathematics.