This work is licensed under aCreative Commons Attribution-Noncommercial-No Derivative Works 4. Partially ordered sets, lattice theory, Boolean algebra, equivalence relationsĬhristianity | Computer Sciences | Mathematicsįrom Discrete Mathematics: An Integrated Approach, a self-published textbook for use in Math 212 Into areas that are of crucial importance to computer science. OurĮxploration of these ideas will nicely tie together some earlier ideas in logic and set theory as well as lead us Order-structures (posets, lattices) and to introduce an abstract type of algebra known as Boolean Algebra. Particularly ones that impose an order of one sort or another on a set. In this chapter we will explore other kinds of relations (these will all be binary relations here), We began discussing this topic in the last chapter when we introduced equivalence Many contemporary mathematical applications involve binary or n-ary relations inĪddition to computations. Relational ideas have become more important with the advent of computer science and the rise of discrete ≤, but this almost seems like an intrusion foreign to the main focus, which is making algebraic calculations. Jongsma, Calvin, 'Discrete Mathematics: Chapter 7, Posets, Lattices, & Boolean Algebra' (2016).Faculty Work: Comprehensive List.ĭigitalcollections.dordt/faculty_work/ Discrete Mathematics: Chapter 7, Posets, Lattices, & Boolean AlgebraĪlgebra deals with more than computations such as addition or exponentiation it also studies relations.Ĭalculus touches on this a bit with locating extreme values and determining where functions increase andĭecrease and in elementary algebra you occasionally “solve” inequalities involving the order relations of < or For more information, please Recommended Citation It has been accepted for inclusion in Faculty Work:Ĭomprehensive List by an authorized administrator of Digital Collections Dordt.
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This Book Chapter is brought to you for free and open access by Digital Collections Dordt. Our exploration of these ideas will nicely tie together some earlier ideas in logic and set theory as well as lead us into areas that are of crucial importance to computer science.Digital Collections Dordt Faculty Work: Comprehensive List 1- Discrete Mathematics: Chapter 7, Posets, Lattices, & Boolean Algebra Calvin Jongsmaĭordt College, Follow this and additional works at:digitalcollections.dordt/faculty_work Part of theChristianity Commons,Computer Sciences Commons, and theMathematics Commons This will lead us to investigate certain order-structures (posets, lattices) and to introduce an abstract type of algebra known as Boolean Algebra. In this chapter we will explore other kinds of relations (these will all be binary relations here), particularly ones that impose an order of one sort or another on a set.
We began discussing this topic in the last chapter when we introduced equivalence relations.
Many contemporary mathematical applications involve binary or n-ary relations in addition to computations. Relational ideas have become more important with the advent of computer science and the rise of discrete mathematics, however. Calculus touches on this a bit with locating extreme values and determining where functions increase and decrease and in elementary algebra you occasionally “solve” inequalities involving the order relations of < or ≤, but this almost seems like an intrusion foreign to the main focus, which is making algebraic calculations. Algebra deals with more than computations such as addition or exponentiation it also studies relations.
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