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Teaching MAD@ASDonline1 Teaching Discrete Mathematics and Algorithms & Data Structures Online G.MirkowskaPJIIT

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Teaching MAD@ASDonline2 Discrete Mathematics course Discrete Mathematics is a fundamental part of mathematical education for informatitions. Discrete Mathematics is a fundamental part of mathematical education for informatitions. It play an important role in Computer Science. It play an important role in Computer Science. The goal of the lecture is to introduce several fundamental notions and tools: functions, relations, graphs, models, satisfiability, induction etc. The goal of the lecture is to introduce several fundamental notions and tools: functions, relations, graphs, models, satisfiability, induction etc. These notions are key components not only in theoretical computer science, but also in practical computing. These notions are key components not only in theoretical computer science, but also in practical computing.

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Teaching MAD@ASDonline3 DM Aims DM Aims The course is designed to: give a general knowledge about the area of discrete mathematics, give a general knowledge about the area of discrete mathematics, more in-depth knowledge of selected topics, more in-depth knowledge of selected topics, help students to understand abstract notions, help students to understand abstract notions, introduce the methods of proving in mathematics and in computer science. introduce the methods of proving in mathematics and in computer science.

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Teaching MAD@ASDonline4 Learning outcomes After having followed this course, students should understand the basic definitions and concepts, understand the basic definitions and concepts, have knowledge of the basic techniques and know how to apply them, have knowledge of the basic techniques and know how to apply them, be able to understand new situations and concepts, and relate them to existing knowledge; be able to understand new situations and concepts, and relate them to existing knowledge; be able to model actual situations in a mathematical way. be able to model actual situations in a mathematical way.

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Teaching MAD@ASDonline5 DM - Topics covered Algebra of sets Algebra of sets Graphs, basic notions Graphs, basic notions Functions Functions Relations (algebra of relations, orderings, equivalence ) Relations (algebra of relations, orderings, equivalence ) Elements of classical logic Elements of classical logic Induction and recursion Induction and recursion Combinatorics Combinatorics Elements of discrete probability Elements of discrete probability

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Teaching MAD@ASDonline6 Algorithms and Data Structures course This course is an introduction to the design & analysis of wide variety of algorithms. The topic is often called `Algorithmics'. This course is an introduction to the design & analysis of wide variety of algorithms. The topic is often called `Algorithmics'. Emphasis is put on Emphasis is put on specification, specification, matching the appropriate data structures and algorithms to application problems, matching the appropriate data structures and algorithms to application problems, correctness, correctness, complexity analysis. complexity analysis.

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Teaching MAD@ASDonline7 ADS - Course objectives Study efficient algorithms for a number of fundamental problems, Study efficient algorithms for a number of fundamental problems, learn techniques for designing algorithms, learn techniques for designing algorithms, learn fundamental data structures and how to use them in appropriate way, learn fundamental data structures and how to use them in appropriate way, prove software correctness, prove software correctness, analyze running time of algorithms. analyze running time of algorithms.

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Teaching MAD@ASDonline8 Learning outcomes be able to develop efficient algorithms for simple tasks, be able to develop efficient algorithms for simple tasks, be able to specify algorithms and data structures, be able to specify algorithms and data structures, be able to verify correctness of simple algorithms, be able to verify correctness of simple algorithms, understand the concepts of time and space complexity, understand the concepts of time and space complexity, know several representations of data structures and know how and when to use them, know several representations of data structures and know how and when to use them, know and understand the idea of different methods of constructing algorithms, know and understand the idea of different methods of constructing algorithms, understand the notion of tractable and intractable problems. understand the notion of tractable and intractable problems.

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Teaching MAD@ASDonline9 ADS – Topics covered Preliminaries, specification, correctness, complexity Preliminaries, specification, correctness, complexity Searching and Sorting algorithms Searching and Sorting algorithms Data structures (specification, implementation) Data structures (specification, implementation) Tables, stacks, queues Tables, stacks, queues Trees BST, AVL, Heap Trees BST, AVL, Heap Dictionaries, Hash tables Dictionaries, Hash tables Priority queues, Heap Priority queues, Heap Find-Union structure Find-Union structure

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Teaching MAD@ASDonline10 ASD – Topics covered Algorithms on graphs Algorithms on graphs Dijkstra, Kruskal, Prim, Huffman, etc. Dijkstra, Kruskal, Prim, Huffman, etc. Methods of constructing algorithms Methods of constructing algorithms Divide and conquer Divide and conquer Dynamic programming Dynamic programming Greedy strategies Greedy strategies Algorithms in geometry Algorithms in geometry Hard problems Hard problems

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Teaching MAD@ASDonline11 Lectures Details Lectures Details The courses were divided on 15 lectures. The courses were divided on 15 lectures. Each lecture has 5-7 short sections. Each lecture has 5-7 short sections. Pictures Pictures Questions @ Answers Questions @ Answers Problems Problems Examples Examples Presentations.ppt Presentations.ppt The last section is devoted to exercises. The last section is devoted to exercises. Each lecture is supported by a set of questions. Each lecture is supported by a set of questions. lecture presentation aplet sort. aplet heap Quiz

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Teaching MAD@ASDonline12 DM Week schedule One lecture per week One lecture per week Test for 2-3 days (evaluated) Test for 2-3 days (evaluated) usually 5 questions = 5 points usually 5 questions = 5 points many possible answers many possible answers Homework (evaluated in iterative process) Homework (evaluated in iterative process) usually two problems the solutions of which should be written with explanation and sent to the theacher. usually two problems the solutions of which should be written with explanation and sent to the theacher. MTWTFSSuMTWTFS reading lecture tests solving homeworksolveimplement write documentation

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Teaching MAD@ASDonline13 Evaluation -> Conclusion Half of the total number of points allows a student to be accepted for the final exam. Half of the total number of points allows a student to be accepted for the final exam. exams 40 points accepted 20/40 exams 40 points accepted 20/40

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