Discrete Mathematics (MATH 204)

2023 Summer
Faculty of Engineering and Natural Sciences
Mathematics(MATH)
3
6
Canan Kaşıkcı canankasikci@sabanciuniv.edu,
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English
Undergraduate
--
Formal lecture,Recitation
Interactive,Communicative
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CONTENT

Introduction to combinatorial problems and techniques. Sets, relations and functions. Graphs, trees, matching, network flows. Counting techniques. Recurrence relations and generating functions. Combinatorial circuits and finite state machines.

OBJECTIVE

This course aims to introduce basic ideas of discrete mathematics such as formal mathematical reasoning techniques, basic counting techniques, relations, graphs and trees. The course gives students training to develop their mathematical skills, analytical and critical thinking abilities, their ability to apply these capabilities to practical problems, and to communicate their knowledge of these areas.

LEARNING OUTCOMES

  • Understand the notion of mathematical thinking, mathematical proofs, algorithmic thinking, and able to apply them in problem solving, Present simple proofs in a precise and formally correct way, Apply various methods of prof like mathematical induction, direct, indirect proofs.
  • Understand and manipulate sets, sequences and sums.
  • Understand the basic concept of an algorithm and apply appropriate algorithms to solve problems in combinatorial mathematics. Analyze simple algorithms.
  • Have a basic understanding of divisibility and prime numbers, basics of modular arithmetic.
  • Understand all of the basic counting techniques, and some of the advanced counting techniques. Be able to use factorials, binomial coefficients appropriately, solve linear recurrences of small order.
  • Understand the basic properties of graphs and trees and use these concepts to model simple applications.

PROGRAMME OUTCOMES


1. Understand the world, their country, their society, as well as themselves and have awareness of ethical problems, social rights, values and responsibility to the self and to others. 1

2. Understand different disciplines from natural and social sciences to mathematics and art, and develop interdisciplinary approaches in thinking and practice. 4

3. Think critically, follow innovations and developments in science and technology, demonstrate personal and organizational entrepreneurship and engage in life-long learning in various subjects; have the ability to continue to educate him/herself. 2

4. Communicate effectively in Turkish and English by oral, written, graphical and technological means. 3

5. Take individual and team responsibility, function effectively and respectively as an individual and a member or a leader of a team; and have the skills to work effectively in multi-disciplinary teams. 2


1. Possess sufficient knowledge of mathematics, science, fundamental engineering, computational methods and program-specific engineering topics; use theoretical and applied knowledge of these areas in complex engineering problems. 4

2. Identify, define, formulate and solve complex engineering problems while considering the UN Sustainable Development Goals; choose and apply suitable analysis, design, estimation/prediction and modeling methods for this purpose. 3

3. Develop, choose and use modern techniques and tools that are needed for analysis and solution of complex problems faced in engineering applications; use information technologies effectively. 2

4. Have the ability to design a complex system, process, instrument or a product under realistic constraints and conditions, with the goal of fulfilling creative current and future requirements. 1

5. Use research methods, including conducting literature reviews, designing experiments, performing experiments, collecting data, analyzing results, and interpreting results, to investigate complex engineering problems or discipline-specific research topics. 1

6. Possess knowledge of business practices such as project management, risk management, change management, and economic feasibility analysis; awareness on entrepreneurship and innovation. 1

7. Possess knowledge of impact of engineering solutions on society, health and safety, the economy, sustainability, and the environment within the framework of the UN Sustainable Development Goals; awareness on legal outcomes of engineering solutions; awareness of acting impartially and inclusively without any form of discrimination; act in accordance with ethical principles, possessing knowledge of professional and ethical responsibilities. 1

8. Communicate effectively, both orally and in writing, on technical subjects, considering the diverse characteristics of the target audience (such as education, language, and profession). 1


1. Develop knowledge of theories, concepts, and research methods in humanities and social sciences. 4

2. Assess how global, national and regional developments affect society. 2

3. Know how to access and evaluate data from various sources of information. 3


1. Provide constructive analysis of economic phenomena at the national and international level, and interactions between the two. 2

2. Develop an understanding of organizations and institutions in the society as well as their influence on the economy. 2

3. Recognize how incentives shape the behavior of individuals and organizations. 2

4. Identify "economic" problems and propose alternative models and/or design and conduct research to provide viable solutions using theoretical tools and/or quantitative methods. 4

5. Communicate problems and solutions to managerial and policy decision-making units as well as to lay audiences. 3

ASSESSMENT METHODS and CRITERIA

  Percentage (%)
Final 40
Midterm 40
Quiz 15
Participation 5

RECOMENDED or REQUIRED READINGS

Textbook

Kenneth H. Rosen, Discrete Mathematics and Its Applications, McGraw-Hill

Readings

1. Ronald L. Graham, Donald E. Knuth, Oren Patashnik,
Concrete Mathematics, Addison-Wesley

2. Alan Tucker, Applied Combinatorics, John Wiley Sons