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[[Category:MA375Spring2009Walther]] | [[Category:MA375Spring2009Walther]] | ||
| + | [[Category:MA375]] | ||
| + | [[Category:math]] | ||
| + | [[Category:discrete math]] | ||
| + | [[Category:lecture notes]] | ||
| + | ==Adding pages== | ||
| + | [[MA375]] Spring 2009 Prof. Walther | ||
| + | ---- | ||
| + | If you want to add a new page for a definition, remember to put it in double square brackets like this: <nowiki>[[Truth Values]]</nowiki> (it will look like this [[Truth Values]]). Then hit submit, and if it says the page doesn't exist, you can add text to explain the concept. | ||
| + | |||
| + | Note that you should still add the category (in this case <nowiki>[[Category:MA375Spring2009Walther]]</nowiki>) to the new page. If you think the page would apply to the class in general (for example, any MA375 class), add <nowiki>[[Category:MA375]]</nowiki> on the next line. | ||
| + | |||
| + | ==Introduction== | ||
For those of you who like definitions and theorems more than homework | For those of you who like definitions and theorems more than homework | ||
I dedicate this page to you. I intend to get them all with our math brick | I dedicate this page to you. I intend to get them all with our math brick | ||
- I mean book - as a guide before semester's end. | - I mean book - as a guide before semester's end. | ||
| + | |||
You see, I will not be able to use the copyrighted material exactly | You see, I will not be able to use the copyrighted material exactly | ||
from the book, so I (and you if you join me) will have to rewrite, and/or | from the book, so I (and you if you join me) will have to rewrite, and/or | ||
| Line 10: | Line 23: | ||
should not be overly difficult. Let us begin! | should not be overly difficult. Let us begin! | ||
| − | Chapter 1 | + | DEF Discrete mathematics is the branch of mathematics that studies separate entities. |
| + | |||
| + | ==Chapter 1== | ||
| + | |||
| + | DEF [[Truth value]]s are confined to true "T", and false "F". | ||
| + | |||
| + | DEF A letter is an object that is assigned a truth value. | ||
| + | |||
| + | DEF A logical connective stands between two letters, joining them into a statement. It can also join a letter with a statement, or two statements, into a compound statement. | ||
| + | |||
| + | DEF The logical connective "or", denoted "<math>\vee</math>", assigns the truth value T to the statement it creates whenever either of the objects it stands between has a truth value of T. | ||
| + | |||
| + | DEF The logical connective "and", denoted "<math>\wedge</math>", assigns the truth value T to the statement it creates whenever either of the objects it stands between has a truth value of T. | ||
| + | |||
| + | DEF A [[proposition]] is a statement that can be assigned a single truth value. | ||
| + | |||
| + | DEF A proposition's [[negation]] is assigned the truth value the proposition | ||
| + | is not. | ||
| + | |||
| + | DEF A truth table is a list of all possible combinations of truth values for a collection of objects. | ||
| + | |||
| + | DEF A set is a collection of objects. | ||
| + | |||
| + | DEF The empty set is a set that contains no objects. | ||
| + | |||
| + | DEF The cardinality of a set is the number of objects it contains. | ||
| + | |||
| + | DEF Two sets are equal if they contain the same objects. | ||
| + | |||
| + | DEF Set A is a subset of set B if every object in A is also in B. | ||
| + | |||
| + | DEF Set A is a proper subset of set B if set B contains an object not contained in A. | ||
| + | |||
| + | DEF The union of two sets A and B is a set contaning any object that is in A or is in B, or, for clarity in English, in both A and B. | ||
| + | |||
| + | DEF The intersection of sets A nad B is a set containing any object that is in both set A and set B. | ||
| + | |||
| + | |||
| − | + | '''Contributors notes''' | |
| − | + | 20090122? I am stopping here for now, as the next operation involves learning a new skill: that of inserting math symbols into the text. I am already happy enough that this worked, as my previous experience with wikis stops at editing Wikipedia toward Standard American English. I have never before created a page (and actually I did not create this one from whole cloth, but started with a given template.) | |
| − | + | 20090205 Well I can insert math symbols, though displaying insecure items on my machine is not so easy. Now I need to veer away from propositional calculus and move on to set theory I mean graph theory I mean lattices..., did I tell you I went to school (and the occasional math contest?) with Arthur Rubin? He wasn't there much, but it seems he didn't need to be. He could type 90 wpm (but probably not when inserting LaTek symbols :) I do know he was admitted directly to Cal Tech graduate school after his high school graduation. And after looking at Wikipedia I guess he took five years to get his Ph.D.. | |
| − | + | ||
| − | + | 20090219 I've taken three math tests in the last two weeks and I'm happy to report that I got a 100 in MA 353, Linear Algebra II, and a well I got a grade in MA 385, Logic, and well idk what I got in vector calculus (Calculus V at Purdue; is it right to make people suffer through five semesters of calculus?) but I think I got all of the zeroes and none of the ones. I keep digressing on my definitions too. I dropped in a little of what I remember from set theory. You see mathematics should be fun, and too often it is not so if you agree with me use these pages for your thoughts, as well as your homework. | |
| + | ---- | ||
| + | [[MA375_%28WaltherSpring2009%29|Back to MA375, Spring 2009, Prof. Walther]] | ||
Latest revision as of 07:41, 20 May 2013
Adding pages
MA375 Spring 2009 Prof. Walther
If you want to add a new page for a definition, remember to put it in double square brackets like this: [[Truth Values]] (it will look like this Truth Values). Then hit submit, and if it says the page doesn't exist, you can add text to explain the concept.
Note that you should still add the category (in this case [[Category:MA375Spring2009Walther]]) to the new page. If you think the page would apply to the class in general (for example, any MA375 class), add [[Category:MA375]] on the next line.
Introduction
For those of you who like definitions and theorems more than homework I dedicate this page to you. I intend to get them all with our math brick - I mean book - as a guide before semester's end.
You see, I will not be able to use the copyrighted material exactly from the book, so I (and you if you join me) will have to rewrite, and/or go do research for other versions of this material in the public domain. Most of this mathematics will have been extant for some time, so that should not be overly difficult. Let us begin!
DEF Discrete mathematics is the branch of mathematics that studies separate entities.
Chapter 1
DEF Truth values are confined to true "T", and false "F".
DEF A letter is an object that is assigned a truth value.
DEF A logical connective stands between two letters, joining them into a statement. It can also join a letter with a statement, or two statements, into a compound statement.
DEF The logical connective "or", denoted "$ \vee $", assigns the truth value T to the statement it creates whenever either of the objects it stands between has a truth value of T.
DEF The logical connective "and", denoted "$ \wedge $", assigns the truth value T to the statement it creates whenever either of the objects it stands between has a truth value of T.
DEF A proposition is a statement that can be assigned a single truth value.
DEF A proposition's negation is assigned the truth value the proposition is not.
DEF A truth table is a list of all possible combinations of truth values for a collection of objects.
DEF A set is a collection of objects.
DEF The empty set is a set that contains no objects.
DEF The cardinality of a set is the number of objects it contains.
DEF Two sets are equal if they contain the same objects.
DEF Set A is a subset of set B if every object in A is also in B.
DEF Set A is a proper subset of set B if set B contains an object not contained in A.
DEF The union of two sets A and B is a set contaning any object that is in A or is in B, or, for clarity in English, in both A and B.
DEF The intersection of sets A nad B is a set containing any object that is in both set A and set B.
Contributors notes
20090122? I am stopping here for now, as the next operation involves learning a new skill: that of inserting math symbols into the text. I am already happy enough that this worked, as my previous experience with wikis stops at editing Wikipedia toward Standard American English. I have never before created a page (and actually I did not create this one from whole cloth, but started with a given template.)
20090205 Well I can insert math symbols, though displaying insecure items on my machine is not so easy. Now I need to veer away from propositional calculus and move on to set theory I mean graph theory I mean lattices..., did I tell you I went to school (and the occasional math contest?) with Arthur Rubin? He wasn't there much, but it seems he didn't need to be. He could type 90 wpm (but probably not when inserting LaTek symbols :) I do know he was admitted directly to Cal Tech graduate school after his high school graduation. And after looking at Wikipedia I guess he took five years to get his Ph.D..
20090219 I've taken three math tests in the last two weeks and I'm happy to report that I got a 100 in MA 353, Linear Algebra II, and a well I got a grade in MA 385, Logic, and well idk what I got in vector calculus (Calculus V at Purdue; is it right to make people suffer through five semesters of calculus?) but I think I got all of the zeroes and none of the ones. I keep digressing on my definitions too. I dropped in a little of what I remember from set theory. You see mathematics should be fun, and too often it is not so if you agree with me use these pages for your thoughts, as well as your homework.
