{"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":"2026-08-26T15:16:50","modified_gmt":"2026-08-26T15:16:50","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\/08\/2026_Fall_MAT_141_Syllabus.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\/2026\/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><\/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-45a931920409da5ffc9e66002f89aad2\" 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 9\/4<\/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 9\/18<\/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 10\/9<\/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 10\/30<\/a><\/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 12\/4<\/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\/2026\/08\/Presentation___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 9\/4 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":43,"href":"https:\/\/sites.wcsu.edu\/roccac\/wp-json\/wp\/v2\/pages\/657\/revisions"}],"predecessor-version":[{"id":2285,"href":"https:\/\/sites.wcsu.edu\/roccac\/wp-json\/wp\/v2\/pages\/657\/revisions\/2285"}],"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}]}}