Teaching Discrete Mathematics and Algorithms & Data Structures Online

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Teaching Discrete Teaching Discrete Mathematics and Mathematics and Algorithms & Data Algorithms & Data Structures OnlineStructures Online

G.MirkowskaG.MirkowskaPJIITPJIIT

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Discrete Mathematics courseDiscrete Mathematics course

Discrete Mathematics is a fundamental part of Discrete Mathematics is a fundamental part of mathematical education for informatitions.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 The goal of the lecture is to introduce several fundamental notions and tools: functions, fundamental notions and tools: functions, relations, graphs, models, satisfiability, induction relations, graphs, models, satisfiability, induction etc. etc.

These notions are key components not only in These notions are key components not only in theoretical computer science, but also in practical theoretical computer science, but also in practical computing.computing.

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DM AimsDM Aims

The course is designed to: The course is designed to:

give a general knowledge about the area of give a general knowledge about the area of discrete mathematics, 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 introduce the methods of proving in mathematics

and in computer science. and in computer science.

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Learning outcomesLearning outcomes

After having followed this course, students should 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 have knowledge of the basic techniques and

know how to apply them,know how to apply them, be able to understand new situations and be able to understand new situations and

concepts, and relate them to existing knowledge; concepts, and relate them to existing knowledge; be able to model actual situations in a be able to model actual situations in a

mathematical way. mathematical way.

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DM - Topics coveredDM - Topics covered

Algebra of setsAlgebra of sets Graphs, basic notionsGraphs, basic notions FunctionsFunctions Relations (algebra of relations, orderings, Relations (algebra of relations, orderings,

equivalence )equivalence ) Elements of classical logicElements of classical logic Induction and recursionInduction and recursion CombinatoricsCombinatorics Elements of discrete probabilityElements of discrete probability

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Algorithms and Data Structures Algorithms and Data Structures coursecourse

This course is an introduction to the design & This course is an introduction to the design & analysis of wide variety of algorithms. analysis of wide variety of algorithms. The topic is often called `Algorithmics'. The topic is often called `Algorithmics'.

Emphasis is put onEmphasis is put on specification,specification, matching the appropriate data structures and matching the appropriate data structures and

algorithms to application problems,algorithms to application problems, correctness, correctness, complexity analysiscomplexity analysis. .

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ADS - Course objectivesADS - Course objectives

Study efficient algorithms for a number of Study efficient algorithms for a number of fundamental problems, fundamental problems,

learn techniques for designing algorithms, learn techniques for designing algorithms, learn fundamental data structures and how to use learn fundamental data structures and how to use

them in appropriate way, them in appropriate way, prove software correctness, prove software correctness, analyze running time of algorithms. analyze running time of algorithms.

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Learning outcomesLearning outcomes

be able to develop efficient algorithms for simple be able to develop efficient algorithms for simple tasks,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 understand the concepts of time and space

complexity, complexity, know several representations of data structures know several representations of data structures

and know how and when to use them,and know how and when to use them, know and understand the idea of different methods know and understand the idea of different methods

of constructing algorithms,of constructing algorithms, understand the notion of tractable and intractable understand the notion of tractable and intractable

problems. problems.

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ADS – Topics coveredADS – Topics covered

Preliminaries, specification, correctness, Preliminaries, specification, correctness, complexitycomplexity

Searching and Sorting algorithms Searching and Sorting algorithms Data structures (specification, implementation)Data structures (specification, implementation)

Tables, stacks, queuesTables, stacks, queues Trees BST, AVL, HeapTrees BST, AVL, Heap Dictionaries, Hash tablesDictionaries, Hash tables Priority queues, HeapPriority queues, Heap Find-Union structureFind-Union structure

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ASD – Topics coveredASD – Topics covered

Algorithms on graphsAlgorithms on graphs Dijkstra, Kruskal, Prim, Huffman, etc.Dijkstra, Kruskal, Prim, Huffman, etc.

Methods of constructing algorithmsMethods of constructing algorithms Divide and conquer Divide and conquer Dynamic programming Dynamic programming Greedy strategiesGreedy strategies

Algorithms in geometry Algorithms in geometry Hard problemsHard problems

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Lectures DetailsLectures 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.

PicturesPictures Questions @ Answers Questions @ Answers ProblemsProblems ExamplesExamples Presentations .pptPresentations .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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DM Week scheduleDM Week schedule

One lecture per weekOne lecture per week Test for 2-3 days (evaluated)Test for 2-3 days (evaluated)

usually 5 questions = 5 pointsusually 5 questions = 5 points many possible answersmany possible answers

Homework (evaluated in iterative process)Homework (evaluated in iterative process) usually two problems the solutions of which usually two problems the solutions of which

should be written with explanation and sent to should be written with explanation and sent to the theacher.the theacher.

M T W T F S Su M T W T F S Sureading lecture

tests solving

homework

solve solve

implement implement

write write documentationdocumentation

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Evaluation -> ConclusionEvaluation -> Conclusion

Half of the total number of points allows a student Half of the total number of points allows a student to be accepted for the final exam. to be accepted for the final exam.

exams 40 points exams 40 points accepted 20/40accepted 20/40