{"id":9649941,"date":"2019-06-01T00:20:00","date_gmt":"2019-05-31T21:20:00","guid":{"rendered":"http:\/\/iee.it.teithe.gr\/course\/%ce%bc%ce%b1%ce%b8%ce%b7%ce%bc%ce%b1%cf%84%ce%b9%ce%ba%ce%ac-%ce%b9%ce%b9i\/"},"modified":"2023-11-29T10:29:29","modified_gmt":"2023-11-29T07:29:29","slug":"1302","status":"publish","type":"course","link":"https:\/\/www.iee.ihu.gr\/en\/course\/1302\/","title":{"rendered":"Mathematics \u0399\u0399I"},"content":{"rendered":"<p><strong>Elements of Set Theory<\/strong>: Introduction, Definition of Sets, Set operations, Powersets, Enumerable \u2013 non Enumerable Sets, Cardinality of a Set, Relations and Functions, Equivalence Relations, Partial Order Relations.<\/p>\n<p><strong>Propositional Logic<\/strong>: Propositions &#8211; Syntax, Connectives \u2013 Truth Tables, Tautology \u2013 Contradiction, Tautological Equivalence.<\/p>\n<p><strong>Mathematical Induction<\/strong>: Basic and Strong form of Mathematical Induction.<\/p>\n<p><strong>Combinatorial Analysis<\/strong>: Sum and Product Rules, Permutations, Combinations, Balls and Bins.<\/p>\n<p><strong>Generating Functions<\/strong>: \u00a0Ordinary Generating Functions, Properties, Exponential Generating Functions, Application to Combinatorial Analysis.<\/p>\n<p><strong>Recursive Relations<\/strong>: Recursive Sequences and Relations, Solution of Linear Recursive Relations using Generating Functions.<\/p>\n<p><strong>Elements of Graph Theory<\/strong>: Definitions &#8211; Terminology, Directed and Undirected Graphs, Vertex Degree , Paths , Connected Graphs, Subgraphs, Special types of Graphs, Isomorphic Graphs, Euler and Hamilton Cycles, Graphs and Matrices, Shortest Path and Dijkstra\u2019s Algorithm, Trees, Rooted Trees, Weighted Trees, Minimum Spanning Tree, Binary Trees.<\/p>","protected":false},"author":1,"template":"","meta":{"_acf_changed":false,"inline_featured_image":false,"footnotes":""},"class_list":["post-9649941","course","type-course","status-publish","hentry"],"acf":[],"aioseo_notices":[],"post-meta-fields":{"course-semester":["3"],"_course-semester":["field_5d132f2c14d55"],"course-id":["1302"],"_course-id":["field_5d132b9c78b6e"],"course-group":[""],"_course-group":["field_5d14e905fe59a"],"course-type":["\u0393\u03a5"],"_course-type":["field_5d133c6ba1599"],"course-compulsory":["\u03a5\u03a0"],"_course-compulsory":["field_5d146d39805a6"],"course-field":["\u0393\u0393\u0394"],"_course-field":["field_5d146e248f2b3"],"course-ects":["6"],"_course-ects":["field_5d13518794761"],"course-hours-theory":["4"],"_course-hours-theory":["field_5d13521894762"],"course-hours-lab":[""],"_course-hours-lab":["field_5d1468d18a11f"],"_edit_lock":["1718982340:12"],"_edit_last":["11"],"course-school":["School of Engineering"],"_course-school":["field_5d132bf078b70"],"course-dept":["Department of Information and Electronic Engineering"],"_course-dept":["field_5d132c3a78b71"],"course-level":["1"],"_course-level":["field_5d132c5878b72"],"course-lang":["a:1:{i:0;s:2:\"el\";}"],"_course-lang":["field_5d133e246f04b"],"course-erasmus":["0"],"_course-erasmus":["field_5d133e8e6f04c"],"course-url":["https:\/\/exams-iee.the.ihu.gr\/course\/view.php?id=32"],"_course-url":["field_5d133f9b5c292"],"course-prerequisites":[""],"_course-prerequisites":["field_5d13405189c17"],"course-aim":["The course aims to introduce the students to the basic ideas of discrete mathematics such as basic formal logic, counting techniques, graph theory and their applications in computer science. The main goal of the course is to provide students with a good understanding of the basic theory and some applications of discrete mathematics."],"_course-aim":["field_5d1353f985af8"],"course-goal-1":["Understand the basic concepts of naive set theroy and be able to apply set theoretic operations.\u0393\u03bd\u03c9\u03c1\u03af\u03b6\u03b5\u03b9 \u03c4\u03b9\u03c2 \u03b2\u03b1\u03c3\u03b9\u03ba\u03ad\u03c2 \u03ad\u03bd\u03bd\u03bf\u03b9\u03b5\u03c2 \u03c4\u03b7\u03c2 \u03b1\u03c0\u03bb\u03bf\u03ca\u03ba\u03ae\u03c2 \u03b8\u03b5\u03c9\u03c1\u03af\u03b1\u03c2 \u03c3\u03c5\u03bd\u03cc\u03bb\u03c9\u03bd \u03ba\u03b1\u03b9 \u03bd\u03b1  \u03b5\u03c6\u03b1\u03c1\u03bc\u03cc\u03b6\u03b5\u03b9 \u03c0\u03c1\u03ac\u03be\u03b5\u03b9\u03c2 \u03bc\u03b5 \u03b1\u03c5\u03c4\u03ac. Understand the concepts of set cardinality and distinguish fininte - infinite, enumerable and non-enumerable sets. Be able to apply the pigeonhole principle in practical problems. Comprehend the concept of binary relations and particularly partial orders, total orders and equivalences."],"_course-goal-1":["field_5d13546e85af9"],"course-goal-2":["Underastand the syntax and the semantics of the language of Propositional Logic. Be able to establish logical consequenses using the semantic tools of PL. Be able to distinguish tautologies and contradictions."],"_course-goal-2":["field_5d1354f885afa"],"course-goal-3":["Be able to apply the inductive method in order to establish the validity of arguments dependent on natural numbers."],"_course-goal-3":["field_5d13550085afb"],"course-goal-4":["Comprehend the principles and models of combinatorial analysis and be able to employ them in a varierty of real life problems."],"_course-goal-4":["field_5d13550e85afc"],"course-goal-5":["Realize the connection between sequences and generating functions. Be able to apply generating functions in the solution of combinatorial problems and problems involving linear recursive sequences."],"_course-goal-5":["field_5d13551485afd"],"course-goal-6":["Get familiar with graph theory terminology and concepts. and particularly to the ones related to trees. Be able to detect the presence of key features in a graph such as connectivity and Euler\/Hamilton cycles, and compute its chromatic number. Apply well known algorithms (Dijkstra, BFS, DFS, Prim, Kruskal) and realize their applications in applications. Comprehend the concepts of tree graph, rooted tree and binary tree and be able to app;y pre-, in-, post-order traversal algorithms in binary trees."],"_course-goal-6":["field_5d13551b85afe"],"course-goal-7":[""],"_course-goal-7":["field_5d13552385aff"],"course-skills":["Work in multidisciplinary environement\r\nDevelopment of new research ideas\r\nImprovement of open minded, creative and inductive thought"],"_course-skills":["field_5d1355c25aeb4"],"course-teaching-method":["Face to face teaching"],"_course-teaching-method":["field_5d1383ec75a23"],"course-it-methods":["Notes and slides available in electronic form (in greek).\r\nUse of asynchronous learning platform (Moodle)."],"_course-it-methods":["field_5d1384b975a24"],"course-activity-1":["Lectures"],"_course-activity-1":["field_5d1387d7cba43"],"course-activity-workload-1":["52"],"_course-activity-workload-1":["field_5d1388b2cba46"],"course-activity-2":["Communication\/Collaboration"],"_course-activity-2":["field_5d13886ccba44"],"course-activity-workload-2":["108"],"_course-activity-workload-2":["field_5d1388e9cba47"],"course-activity-3":["Self-study"],"_course-activity-3":["field_5d138878cba45"],"course-activity-workload-3":["20"],"_course-activity-workload-3":["field_5d13890dcba49"],"course-activity-4":[""],"_course-activity-4":["field_5d138947cba4b"],"course-activity-workload-4":[""],"_course-activity-workload-4":["field_5d13891dcba4a"],"course-activity-5":[""],"_course-activity-5":["field_5d14ed2508982"],"course-activity-workload-5":[""],"_course-activity-workload-5":["field_5d14ed3708983"],"course-student-evaluation":["The final exam consists of 7-8 thought development exercises, on the following subjects:\r\n\r\n- Propositional Logic\r\n- Binary Relation\r\n- Pigeonhole Principle\r\n- Induction\r\n- Combinatorics\r\n- Recursive relations\r\n- Generating Functions\r\n- Graph Theory\r\n\r\nThe above examination scheme is communicated to the students through:\r\n\r\n(a) The course web page\r\n(b) The asynchronous learning platform Moodle\r\n(c) Announcements at the begining of the semester and during the lectures."],"_course-student-evaluation":["field_5d1389cff8c01"],"course-eudoxus-bib":["EPP, SUSANNA S., \u0394\u03b9\u03b1\u03ba\u03c1\u03b9\u03c4\u03ac \u039c\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03ac \u03bc\u03b5 \u0395\u03c6\u03b1\u03c1\u03bc\u03bf\u03b3\u03ad\u03c2, 3\u03b7 \u03ad\u03ba\u03b4\u03bf\u03c3\u03b7, \u0395\u03ba\u03b4\u03cc\u03c3\u03b5\u03b9\u03c2 \u039a\u03bb\u03b5\u03b9\u03b4\u03ac\u03c1\u03b9\u03b8\u03bc\u03bf\u03c2, 2010, ISBN 978-960-461-325-0, [\u039a\u03c9\u03b4. \u0395\u03c5\u03b4\u03cc\u03be\u03bf\u03c5 13953].\r\n\u039a\u03b1\u03c4\u03c9\u03c0\u03cc\u03b4\u03b7\u03c2 \u039a\u03c9\u03bd\u03c3\u03c4\u03b1\u03bd\u03c4\u03af\u03bd\u03bf\u03c2 \u03a3\u03c0., \u0395\u03b9\u03c3\u03b1\u03b3\u03c9\u03b3\u03ae \u03c3\u03c4\u03b1 \u03b4\u03b9\u03b1\u03ba\u03c1\u03b9\u03c4\u03ac \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03ac, \u0395\u03ba\u03b4\u03cc\u03c4\u03b7\u03c2: \u0396\u03ae\u03c4\u03b7 \u03a0\u03b5\u03bb\u03b1\u03b3\u03af\u03b1 &amp; \u03a3\u03b9\u03b1 \u0399.\u039a.\u0395., 1\u03b7 \u03ad\u03ba\u03b4., 2015, ISBN: 978-960-456-446-0, [\u039a\u03c9\u03b4. \u0395\u03c5\u03b4\u03cc\u03be\u03bf\u03c5 50658666]."],"_course-eudoxus-bib":["field_5d138e0af441c"],"course-greek-bib":["LIU C., \u03a3\u03c4\u03bf\u03b9\u03c7\u03b5\u03af\u03b1 \u0394\u03b9\u03b1\u03ba\u03c1\u03b9\u03c4\u03ce\u03bd \u039c\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03ce\u03bd, \u03a0\u03b1\u03bd\u03b5\u03c0\u03b9\u03c3\u03c4\u03b7\u03bc\u03b9\u03b1\u03ba\u03ad\u03c2 \u0395\u03ba\u03b4\u03cc\u03c3\u03b5\u03b9\u03c2 \u039a\u03c1\u03ae\u03c4\u03b7\u03c2, 2009, ISBN 978-960-524-072-1\r\nROSEN K., \u0394\u03b9\u03b1\u03ba\u03c1\u03b9\u03c4\u03ac \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03ac \u03ba\u03b1\u03b9 \u03b5\u03c6\u03b1\u03c1\u03bc\u03bf\u03b3\u03ad\u03c2 \u03c4\u03bf\u03c5\u03c2, 7\u03b7 \u03ad\u03ba\u03b4\u03bf\u03c3\u03b7, \u0395\u03ba\u03b4\u03cc\u03c3\u03b5\u03b9\u03c2 \u03a4\u03b6\u03b9\u03cc\u03bb\u03b1 &amp; \u03a5\u03b9\u03bf\u03b9 \u0391.\u0395., 2014, ISBN: 978-960-418-394-4.\r\n\u039a\u03c5\u03c1\u03bf\u03cd\u03c3\u03b7\u03c2 \u039b.\u039c., \u039c\u03c0\u03bf\u03cd\u03c1\u03b1\u03c2 \u03a7.\u0399., \u03a3\u03c0\u03c5\u03c1\u03ac\u03ba\u03b7\u03c2 \u03a0.\u0393., \u0394\u03b9\u03b1\u03ba\u03c1\u03b9\u03c4\u03ac \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03ac. \u03a4\u03b1 \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03ac \u03c4\u03b7\u03c2 \u03b5\u03c0\u03b9\u03c3\u03c4\u03ae\u03bc\u03b7\u03c2 \u03c4\u03c9\u03bd \u03c5\u03c0\u03bf\u03bb\u03bf\u03b3\u03b9\u03c3\u03c4\u03ce\u03bd, Gutenberg, 1994, ISBN 978-960-01-0661-4.\r\n\u0391\u03b3\u03b3\u03b5\u03bb\u03ae\u03c2 \u0395.\u03a3.,\u039c\u03c0\u03bb\u03ad\u03c1\u03b7\u03c2 \u0393.\u039b., \u0394\u03b9\u03b1\u03ba\u03c1\u03b9\u03c4\u03ac \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03ac, \u0395\u03ba\u03b4\u03cc\u03c3\u03b5\u03b9\u03c2 \u03a4\u03b6\u03b9\u03cc\u03bb\u03b1, 2003, ISBN 960-418-009-6."],"_course-greek-bib":["field_5d138e3cf441d"],"course-intl-bib":["EPP, SUSANNA S.: Discrete Mathematics with Applications, Wadsworth, 1990, ISBN 0495391328\r\nGRAHAM, R., KNUTH, D., PATASHNIK, O.:  Concrete Mathematics, Addison Wesley, 1994.\r\nROSEN K.H., Discrete mathematics and its applications. New York: McGraw-Hill, 2012.\r\nGRIMALDI, R.: Discrete and Combinatorial Mathematics. An Applied Introduction, Addison Wesley, 1994.\r\nHALL, M., Jr.:  Combinatorial Theory, John Wiley &amp; Sons, 1986.\r\nHARARY, F.:  Graph Theory, John Wiley &amp; Sons, 1986.\r\nLIPSCHUTZ, S.: Set Theory, McGraw Hill, 1964.\r\nLIU, C.: Introduction to Combinatorial Mathematics, McGraw Hill, 1968.\r\nLIU, C.: Elements of Discrete Mathematics, McGraw Hill, 1986.\r\nREINGOLD, M., NIERERGELT, J., DEO, N.: Combinatorial Algorithms Theory and Practice, Prentice Hall, 1977.\r\nROSS, K. A., WRIGTH, C. R. B. : Discrete Mathematics, Prentice Hall, 1992.\r\nTOMESCU, I. And MELTER, R.: Problems in Combinatorial and Graph Theory, John Wiley &amp; Sons, 1985.\r\nWITALA, S, A.: Discrete Mathematics. A Unified Approach, McGraw Hill, 1987."],"_course-intl-bib":["field_5d138e74f441e"],"course-rel-journals":[""],"_course-rel-journals":["field_5d138ec4f441f"],"course-teachers":["a:1:{i:0;s:7:\"9651009\";}"],"_course-teachers":["field_5d3aa2923f803"],"_wp_old_slug":["%ce%bc%ce%b1%ce%b8%ce%b7%ce%bc%ce%b1%cf%84%ce%b9%ce%ba%ce%ac-%ce%b9%ce%b9i"],"course-coordinator":["a:1:{i:0;s:7:\"9650977\";}"],"_course-coordinator":["field_5faa4466f1b87"],"_aioseo_title":[null],"_aioseo_description":[null],"_aioseo_keywords":[""],"_aioseo_og_title":[null],"_aioseo_og_description":[null],"_aioseo_og_article_section":[""],"_aioseo_og_article_tags":[""],"_aioseo_twitter_title":[null],"_aioseo_twitter_description":[null]},"_links":{"self":[{"href":"https:\/\/www.iee.ihu.gr\/en\/wp-json\/wp\/v2\/course\/9649941","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.iee.ihu.gr\/en\/wp-json\/wp\/v2\/course"}],"about":[{"href":"https:\/\/www.iee.ihu.gr\/en\/wp-json\/wp\/v2\/types\/course"}],"author":[{"embeddable":true,"href":"https:\/\/www.iee.ihu.gr\/en\/wp-json\/wp\/v2\/users\/1"}],"version-history":[{"count":0,"href":"https:\/\/www.iee.ihu.gr\/en\/wp-json\/wp\/v2\/course\/9649941\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.iee.ihu.gr\/en\/wp-json\/wp\/v2\/media?parent=9649941"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}