Propositional Equivalences An important type of step used in a mathematical argument is the replacement of a statement with another statement with the same truth value. Note that we will use the term “compound proposi- tion” to refer to an expression formed from propositional variables using logical operators, such as p ∧ q. Tautology: compound proposition that is always true Contradiction: compound proposition that is always false Contingency: compound proposition that is neither tautology nor a contradiction Logical Equivalences Compound propositions that have the same truth values in all possible cases are called logically equivalent. We can also define this notion as follows: > The compound propositions p and q are called logically equivalent if p ↔ q is a tautology. The notation p ≡ q denotes that p and q are logically equivalent. Propositional Satisfiability An unsatisfiable compound proposition happens when the negation is a tautology. A satisfiable...
Algorithms and Data Structures 1 [CM1035] Course Description The study of algorithms and data structures is central to an undergraduate degree in computer science. This course will introduce you to your first algorithms and data structures, as well as the tools of abstraction required to help you decide which of these concepts to use. In this way you will not only enhance your box of problem solving tools, you will be able to critically compare, and assess the advantages and disadvantages, of these tools. The course starts at a basic level by describing problems and algorithms in computer science. It then goes on to introduce the tools for describing algorithms: flowcharts and pseudocode. You will then build on these basics to cover a wide range of topics: Abstract data structures such as vectors, queues and stacks. Implementation of abstract data structures with arrays and linked lists. Searching algorithms: Linear Search and Binary Search. Sorting algorithms: Bubble Sort,...
Course Description Target Audience - Those looking to explore the concepts that underpin modern computer science principles. Learners will begin to appreciate some of the core concepts that form the basis of modern computer systems, how they are designed and built and some of the challenges that they will face in developing their own systems. Content Differentiation - This course covers a variety of concepts, presenting them in a clear, accessible and reasoned way. Concepts are explained through examples and learning is reinforced through a variety of interactive activities. Course Goals and Objectives Upon successful completion of this module, you will be able to: Understand the core concepts that underpin modern computer science. Explain, describe and employ different techniques in both a theoretical and practical way. Appreciate how more complex techniques employ the fundamentals that are covered in this course. Textbook and Readings Specific essential readi...
Comments
Post a Comment