{"id":657,"date":"2021-08-05T13:38:31","date_gmt":"2021-08-05T13:38:31","guid":{"rendered":"https:\/\/sites.wcsu.edu\/roccac\/?page_id=657"},"modified":"2026-04-07T20:57:16","modified_gmt":"2026-04-07T20:57:16","slug":"foundational-discrete-mathematics","status":"publish","type":"page","link":"https:\/\/sites.wcsu.edu\/roccac\/homepage\/foundational-discrete-mathematics\/","title":{"rendered":"Foundational Discrete Mathematics"},"content":{"rendered":"\n<h1 class=\"wp-block-heading has-text-color\" style=\"color:#002856\"><strong><a href=\"https:\/\/sites.wcsu.edu\/roccac\/wp-content\/uploads\/sites\/33\/2026\/01\/MAT-141-01-S26-CR.pdf\" data-type=\"link\" data-id=\"https:\/\/sites.wcsu.edu\/roccac\/wp-content\/uploads\/sites\/33\/2024\/01\/2024_Spring_MAT_141_Discrete_Math_Syllabus.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">Syllabus<\/a><\/strong><\/h1>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\" \/>\n\n\n\n<h1 class=\"wp-block-heading\"><a href=\"https:\/\/sites.wcsu.edu\/roccac\/wp-content\/uploads\/sites\/33\/2025\/08\/MAT_141__Foundational_Discrete_Math_Notes.pdf\" data-type=\"link\" data-id=\"https:\/\/sites.wcsu.edu\/roccac\/wp-content\/uploads\/sites\/33\/2025\/08\/MAT_141__Foundational_Discrete_Math_Notes.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><strong>Full Notes Packet<\/strong><\/a><\/h1>\n\n\n\n<ul class=\"wp-block-list\">\n<li>If you find errors in the notes for MAT 141 Foundational Discrete Mathematics, then please fill out the following form: <a href=\"https:\/\/forms.office.com\/r\/y8vLJwZvSS\" target=\"_blank\" rel=\"noreferrer noopener\">https:\/\/forms.office.com\/r\/y8vLJwZvSS<\/a>. Each error submitted can earn you an extra 0.5% on your grade up to +3% extra total.<\/li>\n\n\n\n<li>If you are comfortable DOING SO, you can instead create an &#8220;issue&#8221; on the GitHub repository where the code for the notes is stored: <a href=\"https:\/\/github.com\/cfroccajr\/MAT-141-Foundational-Discrete-Math-Notes\/issues\" target=\"_blank\" rel=\"noreferrer noopener\">https:\/\/github.com\/cfroccajr\/MAT-141-Foundational-Discrete-Math-Notes\/issues<\/a><\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-css-opacity is-style-wide\" \/>\n\n\n\n<h1 class=\"wp-block-heading\"><span style=\"color:#002856\" class=\"tadv-color\">Class Calendar<\/span><\/h1>\n\n\n\n<p>There is a proposed calendar on the syllabus, but here I will record what we actually get through in each class.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>&#8230;<\/li>\n\n\n\n<li>4\/7\/2026: Today we spent more time discussing relations and the properties: reflexive (\\(a\\sim a\\)), symmetric (\\(a\\sim b\\rightarrow b\\sim a\\)), transitive (\\(a\\sim b \\wedge b\\sim c\\rightarrow a\\sim c\\)), and anti-symmetric (\\(a\\sim b \\wedge b\\sim a\\rightarrow a=b\\)). We will look at ways to visualize relations as graphs and start discussing functions on Friday. We are about two classes behind where we should be so we are pushing the due date for the <strong><span style=\"text-decoration: underline\"><em>Unit 3 Practice Exam to 4\/17 and the Unit 3 Exam to 4\/21<\/em><\/span><\/strong>.<\/li>\n\n\n\n<li>3\/31\/2026: You got back the Unit 2 Exams, please try to get the redos to me by 4\/7\/2026.  We also learned more about sets including Cartesian Products and Power Sets.  We then started discussing Relations.<\/li>\n\n\n\n<li>3\/27\/2026: You completed the Unit 2 Exam<\/li>\n\n\n\n<li>3\/24\/2026: Unit 2 Practice Exam Due and Start discussing Sets<\/li>\n\n\n\n<li>3\/13\/2026: More Iteration Examples (End of Unit 2) <\/li>\n\n\n\n<li>3\/10\/2026: Arithmetic and Geometric Sums and Intro to Iteration<\/li>\n\n\n\n<li>3\/6\/2026: Due to the snow day the calendar will be updated as follows:\n<ol class=\"wp-block-list\">\n<li>3\/6\/2026: Recursive Sequences and Intro to Sums and Products<\/li>\n\n\n\n<li>3\/10\/2026: Arithmetic and Geometric Sums and Intro to Iteration<\/li>\n\n\n\n<li>3\/13\/2026: More Iteration Examples (End of Unit 2) and Start discussing Sets and Relations (start of unit 3)<\/li>\n\n\n\n<li>3\/24\/2026: Unit 2 Practice Exam Due and further discussion of relations and their properties<\/li>\n\n\n\n<li>3\/27\/2026: Unit 2 Exam<\/li>\n<\/ol>\n<\/li>\n\n\n\n<li>3\/3\/2026: <img loading=\"lazy\" decoding=\"async\" width=\"25\" height=\"25\" class=\"wp-image-1326\" style=\"width: 25px\" src=\"https:\/\/sites.wcsu.edu\/roccac\/wp-content\/uploads\/sites\/33\/2024\/02\/snow_day-e1769439819504.png\" alt=\"picture of a snowing cloud\"> Snow Day <img loading=\"lazy\" decoding=\"async\" width=\"25\" height=\"25\" class=\"wp-image-1326\" style=\"width: 25px\" src=\"https:\/\/sites.wcsu.edu\/roccac\/wp-content\/uploads\/sites\/33\/2024\/02\/snow_day-e1769439819504.png\" alt=\"picture of a snowing cloud\"><\/li>\n\n\n\n<li>2\/27\/2026: Assuming we have class tomorrow, I will be handing back the first exam. At the top of the exam you will have a grade on the exam and a list of questions to redo in order to earn back up to 40% of the points you lost on the exam. <em><strong>As it says on the syllabus<\/strong><\/em>: Redos are due one week after I hand back the exam, that means I expect them back by Friday 3\/6\/2026, you must turn in the original exam stapled to the top of the redos, for each question you redo you must include a sentence or two explaining what you did wrong, and as out of class work, the quality of your work on redos counts for 10% of the grade. <br>Please note that if you didn&#8217;t turn in the practice exam on Tuesday or Friday you will have a grade of zero; <strong><em>as it says on the syllabus<\/em><\/strong>, practice exams are not accepted after the exam.<br>We will also start covering the material in Unit 2 on Sequences and Sums.<\/li>\n\n\n\n<li>2\/24\/2026:<img loading=\"lazy\" decoding=\"async\" width=\"25\" height=\"25\" class=\"wp-image-1326\" style=\"width: 25px\" src=\"https:\/\/sites.wcsu.edu\/roccac\/wp-content\/uploads\/sites\/33\/2024\/02\/snow_day-e1769439819504.png\" alt=\"picture of a snowing cloud\"> Snow Day <img loading=\"lazy\" decoding=\"async\" width=\"25\" height=\"25\" class=\"wp-image-1326\" style=\"width: 25px\" src=\"https:\/\/sites.wcsu.edu\/roccac\/wp-content\/uploads\/sites\/33\/2024\/02\/snow_day-e1769439819504.png\" alt=\"picture of a snowing cloud\"><\/li>\n\n\n\n<li>2\/20\/2026: Logic Exam (Exam 1)<\/li>\n\n\n\n<li>2\/17\/2026: We completed the last little bit of Unit 1 in time for the exam on Friday.<\/li>\n\n\n\n<li>2\/10\/2026: We started discussing predicates and truth sets.  We will pick up on Friday with further discussion of predicates and quantifiers.  If you are redoing the Writing Assignment please turn it in by next Tuesday 2\/17\/2026.<\/li>\n\n\n\n<li>2\/6\/2026: We discussed valid logical arguments, both basic ones like Modus Ponens, and combinations of arguments like the two column proofs we looked at.<\/li>\n\n\n\n<li>2\/3\/2026: We covered the material on conditionals though the discussion on Modus Ponens, Modus Tollens, the Converse Error, and the Inverse Error.  This included a discussion of when a implication, \\(P\\rightarrow Q\\), is true or false and of the converse, inverse, contrapositive, and negation of the implication.  If you have not already brought in a three ring binder to pick up a notes packet then you need to do so as soon as possible so you can better follow along in class.<\/li>\n\n\n\n<li>1\/30\/2026: We went over the first few pages of the notes packet; up to the page with lists of logical rules.  If you have not already done so you need to bring in a three ring binder to hold the notes.<\/li>\n\n\n\n<li>1\/27\/2026: Today we covered more notation including more practice with set builder notation, interval notation, Cartesian Products of sets (\\(A\\times B\\)), functions, relations, universal quantifiers (\\(\\forall\\)), and existential quantifiers (\\(\\exists\\)).<\/li>\n\n\n\n<li>1\/23\/2026: Today we went over the syllabus, discussed set roster and builder notation, and briefly discussed ands (\\(\\wedge\\)), ors (\\(\\vee\\)), intersections (\\(\\cap\\)), and unions (\\(\\cup\\)).  We also reviewed the sets \\(\\mathbb{N}\\), \\(\\mathbb{Z}\\), \\(\\mathbb{Q}\\), \\(\\mathbb{R}\\), and \\(\\mathbb{C}\\).<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\" \/>\n\n\n\n<h1 class=\"wp-block-heading\"><span style=\"color:#002856\" class=\"tadv-color\">Unit 1: Logic<\/span><\/h1>\n\n\n\n<h4 class=\"wp-block-heading has-text-color has-link-color wp-elements-bd18e956a5865faa7e85cc74bc62b128\" style=\"color:#002856\"><a href=\"https:\/\/sites.wcsu.edu\/roccac\/wp-content\/uploads\/sites\/33\/2025\/01\/Writing_Up_Mathematics_Assessment_Tool-1.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">Writing Up Mathematics Assignment Due 2\/3<\/a><\/h4>\n\n\n\n<h4 class=\"wp-block-heading has-text-color\" style=\"color:#002856\"><a href=\"https:\/\/sites.wcsu.edu\/roccac\/wp-content\/uploads\/sites\/33\/2025\/01\/MAT_141_Unit_I_Study_Guide__Spring_2025_Edition_.pdf\" data-type=\"link\" data-id=\"https:\/\/sites.wcsu.edu\/roccac\/wp-content\/uploads\/sites\/33\/2025\/01\/MAT_141_Unit_I_Study_Guide__Spring_2025_Edition_.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">Practice Exam for Unit 1 Due 2\/17<\/a><\/h4>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\" \/>\n\n\n\n<h1 class=\"wp-block-heading has-text-color\" style=\"color:#002856\">Unit 2: Sequences and Summations<\/h1>\n\n\n\n<h4 class=\"wp-block-heading has-text-color\" style=\"color:#002856\"><a href=\"https:\/\/sites.wcsu.edu\/roccac\/wp-content\/uploads\/sites\/33\/2025\/03\/MAT_141_Unit_II_Study_Guide__Spring_2025_.pdf\" data-type=\"link\" data-id=\"https:\/\/sites.wcsu.edu\/roccac\/wp-content\/uploads\/sites\/33\/2025\/03\/MAT_141_Unit_II_Study_Guide__Spring_2025_.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">Practice Exam for Unit 2 Due 3\/24<\/a><\/h4>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\" \/>\n\n\n\n<h1 class=\"wp-block-heading has-text-color\" style=\"color:#002856\">Unit 3: Sets, Functions, Relations<\/h1>\n\n\n\n<h4 class=\"wp-block-heading has-text-color\" style=\"color:#002856\"><a href=\"https:\/\/sites.wcsu.edu\/roccac\/wp-content\/uploads\/sites\/33\/2026\/01\/2025_Spring_MAT_141_Unit_III_Study_Guide.pdf\" data-type=\"link\" data-id=\"https:\/\/sites.wcsu.edu\/roccac\/wp-content\/uploads\/sites\/33\/2025\/03\/2025_Spring_MAT_141_Unit_III_Study_Guide.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">Practice Exam for Unit 3 Due 4\/17\/2026<\/a> and the Exam will be on 4\/21\/2026.<\/h4>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\" \/>\n\n\n\n<p>Extra Credit Exercise: The code below will build the equivalence classes from #26 in sec. 8.2. Explain how the code works both practically and based on the definition of the relation in 26.<\/p>\n\n\n\n<pre class=\"wp-block-code\" style=\"font-size:13px\"><code># Written in Python\n# Empty collection of equivalence classes\nEC={}\n# Build equivalence classes\nfor i in range(3):\n    for j in range(3):\n        for k in range(3):\n            for l in range(3):\n                # New element\n                temp_lst=&#091;i,j,k,l]\n                # Assign to equivalence class based on sum\n                EC&#091;sum(temp_lst)]=EC.get(sum(temp_lst),&#091;])+&#091;temp_lst]\n# Display equivalence classes\nfor key in EC: print(key,\":\\t\",EC&#091;key])<\/code><\/pre>\n\n\n\n<hr class=\"wp-block-separator has-css-opacity is-style-wide\" \/>\n\n\n\n<h1 class=\"wp-block-heading has-text-color\" style=\"color:#002856\">Unit 4: Counting, Combinatorics, and Graphs<\/h1>\n\n\n\n<h4 class=\"wp-block-heading has-text-color\" style=\"color:#002856\"><a href=\"https:\/\/sites.wcsu.edu\/roccac\/wp-content\/uploads\/sites\/33\/2026\/01\/MAT_141_Unit_IV_Study_Guide__Spring_2025_.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">Practice Exam for Unit 4 Due 5\/8<\/a><\/h4>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\" \/>\n\n\n\n<h1 class=\"wp-block-heading has-text-color\" style=\"color:#002856\">Extra Credit:<\/h1>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"tadv-color\" style=\"color:#ee4d00\">Typesetting Out-of-Class Work in \\(\\LaTeX\\) (+5% on each typed up piece of work)<\/span><\/h2>\n\n\n\n<p>If you are doing this extra credit here is a quick reference sheet with symbols and such: <a href=\"https:\/\/sites.wcsu.edu\/roccac\/wp-content\/uploads\/sites\/33\/2023\/01\/LaTeX_Quick_Reference.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><em><span class=\"tadv-color\" style=\"color:#ee4d00\"><strong>Quick Reference<\/strong><\/span><\/em><\/a><\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><span class=\"tadv-color\" style=\"color:#002856\"><em>Create an account at <a href=\"http:\/\/overleaf.com\" target=\"_blank\" rel=\"noreferrer noopener\">Overleaf.com<\/a> using your WCSU email account<\/em><\/span><\/li>\n\n\n\n<li>Watch the introductory video here <a href=\"https:\/\/media.wcsu.edu\/media\/Using+the+Homework+Template\/1_ij1s2qy2\" target=\"_blank\" rel=\"noreferrer noopener\"><strong><em><span style=\"color:#ee4d00\" class=\"tadv-color\">VIDEO LINK<\/span><\/em><\/strong><\/a>, the document created in the video is here: <a rel=\"noreferrer noopener\" href=\"https:\/\/www.overleaf.com\/read\/khbktbvvvkjd\" target=\"_blank\"><strong><em><span style=\"color:#ee4d00\" class=\"tadv-color\">https:\/\/www.overleaf.com\/read\/khbktbvvvkjd<\/span><\/em><\/strong><\/a><\/li>\n\n\n\n<li><span class=\"tadv-color\" style=\"color:#002856\">Follow this link to see samples of typed up exercises: <\/span><a href=\"https:\/\/www.overleaf.com\/latex\/templates\/homework-template-with-samples\/zmmdzbkzvtzk\" target=\"_blank\" rel=\"noreferrer noopener\">https:\/\/www.overleaf.com\/latex\/templates\/homework-template-with-samples\/zmmdzbkzvtzk<\/a><\/li>\n\n\n\n<li><span style=\"color:#002856\" class=\"tadv-color\">Follow this link to make a copy of a blank template:<\/span> <a rel=\"noreferrer noopener\" href=\"https:\/\/www.overleaf.com\/read\/hwdhcvmntrvs\" target=\"_blank\"><span style=\"color:#ee4d00\" class=\"tadv-color\"><strong><em>https:\/\/www.overleaf.com\/read\/hwdhcvmntrvs<\/em><\/strong><\/span><\/a><\/li>\n\n\n\n<li><span style=\"color:#002856\" class=\"tadv-color\">Submit work by downloading a copy of the PDF you generate and printing it.<\/span><\/li>\n<\/ol>\n\n\n\n<p>If you are having problems typing up a document and would like feedback you can share a link to it by following the directions here: <a href=\"https:\/\/www.overleaf.com\/learn\/how-to\/Sharing_a_project\" target=\"_blank\" rel=\"noreferrer noopener\"><strong><em>https:\/\/www.overleaf.com\/learn\/how-to\/Sharing_a_project<\/em><\/strong><\/a>; send me the link to view but not edit.  You can see a full playlist of video lessons here: <a href=\"https:\/\/media.wcsu.edu\/playlist\/dedicated\/1_m067qwdq\/\" target=\"_blank\" rel=\"noreferrer noopener\">Technical Typesetting with \\(LaTeX\\) Playlist<\/a><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\" \/>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Additional Extra Credit:<\/strong> <\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Complete this <a href=\"https:\/\/sites.wcsu.edu\/roccac\/wp-content\/uploads\/sites\/33\/2025\/10\/Reflecting_on_Quantifiers.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">Reflection on Quantifiers<\/a> for upto +2% on your final grade.<\/li>\n\n\n\n<li>&#8230;<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\" \/>\n\n\n\n<h1 class=\"wp-block-heading\"><span style=\"color:#002856\" class=\"tadv-color\">Links and Handouts<\/span><\/h1>\n\n\n\n<ul class=\"wp-block-list\">\n<li><a rel=\"noopener\" href=\"https:\/\/sites.wcsu.edu\/roccac\/wp-content\/uploads\/sites\/33\/2021\/08\/Set-Laws.pdf\" target=\"_blank\">Sets Reference Table<\/a><\/li>\n\n\n\n<li><a rel=\"noopener\" href=\"https:\/\/sites.wcsu.edu\/roccac\/wp-content\/uploads\/sites\/33\/2021\/08\/PotsdamTables.pdf\" target=\"_blank\">Logic Reference Table<\/a><\/li>\n\n\n\n<li><a rel=\"noopener\" href=\"https:\/\/sites.wcsu.edu\/roccac\/wp-content\/uploads\/sites\/33\/2021\/09\/Blank_Truth_Tables.pdf\" target=\"_blank\">Blank Truth Tables<\/a><\/li>\n\n\n\n<li><a rel=\"noopener\" href=\"https:\/\/sites.wcsu.edu\/roccac\/wp-content\/uploads\/sites\/33\/2021\/08\/ProbabilityNotes.pdf\" target=\"_blank\">Probability Notes<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/math.hmc.edu\/su\/wp-content\/uploads\/sites\/10\/2020\/06\/Writing-Math-Well-HMC-Math.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">\u201cWriting Mathematics Well\u201d<\/a>&nbsp;and&nbsp;<a href=\"https:\/\/math.hmc.edu\/su\/wp-content\/uploads\/sites\/10\/2020\/08\/Guidelines-for-Good-Mathematical-Writing.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">\u201cGuidelines for Good Mathematical Writing\u201d<\/a>&nbsp;by Francis Su<\/li>\n\n\n\n<li><a href=\"https:\/\/sites.wcsu.edu\/roccac\/wp-content\/uploads\/sites\/33\/2025\/01\/Writing_Up_Mathematics_Assessment_Tool-1.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">Writing up Mathematics Packet<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/sites.wcsu.edu\/roccac\/wp-content\/uploads\/sites\/33\/2023\/08\/Beamer_Writing_Up_a_Math_Problem.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">Writing up Mathematics Presentation<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/media.wcsu.edu\/playlist\/dedicated\/1_m067qwdq\/\" target=\"_blank\" rel=\"noreferrer noopener\">Technical Typesetting with \\(LaTeX\\) Playlist<\/a><\/li>\n\n\n\n<li><a href=\"http:\/\/overleaf.com\/\" target=\"_blank\" rel=\"noreferrer noopener\">Overleaf: LaTeX Document Preparation<\/a><\/li>\n\n\n\n<li><a rel=\"noreferrer noopener\" href=\"https:\/\/www.youtube.com\/c\/WritelatexOnline\/videos\" target=\"_blank\">Overleaf Tutorial Videos<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/media.wcsu.edu\/playlist\/dedicated\/1_m067qwdq\/\" target=\"_blank\" rel=\"noreferrer noopener\"><\/a><a href=\"http:\/\/www.utc.fr\/~jlaforet\/Suppl\/latex-cheatsheet.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">LaTeX Quick Reference<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/sites.wcsu.edu\/roccac\/wp-content\/uploads\/sites\/33\/2023\/01\/LaTeX_Quick_Reference.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">LaTeX Quick Reference v.2<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.overleaf.com\/latex\/templates\/homework-template-with-samples\/zmmdzbkzvtzk\" target=\"_blank\" rel=\"noreferrer noopener\">Homework Template with Samples<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.overleaf.com\/read\/hwdhcvmntrvs\" target=\"_blank\" rel=\"noreferrer noopener\">Homework Template Blank<\/a><\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-css-opacity is-style-wide\" \/>\n\n\n\n<h1 class=\"wp-block-heading\"><span style=\"color:#002856\" class=\"tadv-color\">Vocabulary<\/span><\/h1>\n\n\n\n<p class=\"has-text-color\" style=\"color:#002658\">\\(\\mathbb{N}\\),&nbsp;\\(\\mathbb{Z}\\),&nbsp;\\(\\mathbb{Q}\\),&nbsp;\\(\\mathbb{R}\\), rational number, irrational number, set notation, set roster notation, modus ponens, modus tollens, De Morgan&#8217;s Law, negation, distribution, commutative law, associative law, \\(\\forall\\), \\(\\exists\\), converse, inverse, contrapositive, conjunction, disjunction,&nbsp; set, subset, Cartesian product, relation, function, sequences, series, summation, summation notation \\[\\sum_{i=0}^n a_i=a_0+a_1+\\cdots+a_n,\\] product notation \\[\\prod_{i=0}^n a_i=a_0\\times a_1\\times \\cdots\\times a_n,\\] geometric sum \\[\\sum_{i=0}^n a\\, r^i=a+ar+ar^2+\\cdots+ar^n=a\\, \\frac{(r^{n+1}-1)}{r-1},\\] union, intersection, set difference, set complement, power set &#8211; \\(\\mathscr{P}(x)\\), reflexive, symmetric, transitive, anti-symmetric, function, one-to-one, onto, inverses, composition, addition principle, multiplication principle, possibilities tree, combinations, factorial, permutations, binomial coefficients, multinomial coefficients, graph, walk, circuit, Euler circuit, path, tree, trail, binary tree, Hamilton circuit, closed walk, \u2026 etc.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Syllabus Full Notes Packet Class Calendar There is a proposed calendar on the syllabus, but here I will record what we actually get through in each class. Unit 1: Logic Writing Up Mathematics Assignment Due 2\/3 Practice Exam for Unit &hellip; <a href=\"https:\/\/sites.wcsu.edu\/roccac\/homepage\/foundational-discrete-mathematics\/\">Continue reading <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":35,"featured_media":0,"parent":2,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"wpo365_audiences":[],"wpo365_private":false,"footnotes":""},"class_list":["post-657","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/sites.wcsu.edu\/roccac\/wp-json\/wp\/v2\/pages\/657","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sites.wcsu.edu\/roccac\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/sites.wcsu.edu\/roccac\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/sites.wcsu.edu\/roccac\/wp-json\/wp\/v2\/users\/35"}],"replies":[{"embeddable":true,"href":"https:\/\/sites.wcsu.edu\/roccac\/wp-json\/wp\/v2\/comments?post=657"}],"version-history":[{"count":30,"href":"https:\/\/sites.wcsu.edu\/roccac\/wp-json\/wp\/v2\/pages\/657\/revisions"}],"predecessor-version":[{"id":2158,"href":"https:\/\/sites.wcsu.edu\/roccac\/wp-json\/wp\/v2\/pages\/657\/revisions\/2158"}],"up":[{"embeddable":true,"href":"https:\/\/sites.wcsu.edu\/roccac\/wp-json\/wp\/v2\/pages\/2"}],"wp:attachment":[{"href":"https:\/\/sites.wcsu.edu\/roccac\/wp-json\/wp\/v2\/media?parent=657"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}