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离散数学

Long Huan 龙环

离散数学是计算机专业基础课程之一。本课程重点讲解离散对象的计数问题、图论问题、网络流问题等计算机科学中的重要基本知识。本课程将为后续如数据结构、算法设计、复杂性理论提供必要的基础，课程内容在人工智能、机器学习、网络设计与分析等前沿领域有重要应用。课程重点培养学生逻辑思维能力及解决问题的能力。

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What's inside

Syllabus

离散数学基础

组合计数

函数估计

图论导引

特殊图

树及算法

网络流

Good to know

Know what's good

, what to watch for

, and possible dealbreakers

Explores counting, graph, and network flow problems, which are core concepts in computer science

Provides a foundation for computer science courses such as data structures, algorithm design, and complexity theory

Applicable to artificial intelligence, machine learning, and network design and analysis

Develops logical thinking and problem-solving abilities

Taught by instructors with expertise in discrete mathematics and computer science

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Reviews summary

Learn discrete math concepts

“离散数学” is an introductory course for undergraduate students in computer science. Concepts taught in this course build a foundation for more advanced classes in data structures, algorithm design, and complexity theory. Though reviews for this course mention a lack of engagement, the course’s content seems to be in line with its description and syllabus. Based on the available reviews, this course does not seem to be particularly difficult, but it also does not seem to be particularly engaging.

Neither too hard nor too easy.

"难点讲的不是特别清楚（可能个人理解问题）"

"然后不是难点的地方又有时候感觉啰嗦了点。"

Low level of student engagement.

"Nobody is here."

Incomplete certificates.

"互评没有人评价，最后证书图片都是不完整的。"

Activities

Be better prepared before your course. Deepen your understanding during and after it. Supplement your coursework and achieve mastery of the topics covered in 离散数学 with these activities:

Review basic probability and statistics concepts

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Brushing up on probability and statistics strengthens the foundation for understanding discrete mathematics.

Browse courses on Probability

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Review textbooks or online resources on probability and statistics
Solve practice problems to reinforce understanding

Follow tutorials to set up a Python environment

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Following tutorials to install necessary software is a key step to ensure seamless learning.

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Research Python environment setup tutorials
Select a tutorial that aligns with your preferred operating system and Python version
Follow the tutorial step-by-step

Review Discrete Mathematics and Its Applications by Kenneth H. Rosen

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Rosen provides clear explanations and comprehensive coverage of discrete mathematics concepts encountered in the course.

View Discrete Mathematics and Its Applications (in... on Amazon

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Read selected chapters relevant to the course material
Study examples and solve practice problems

Five other activities

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Compile notes, assignments, and resources

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Organizing course materials enhances accessibility and simplifies review.

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Gather and整理 notes from lectures and readings
Organize assignments by topic and difficulty
Create a central repository or digital folder for all materials

Solve practice problems on combinatorics

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Practicing combinatorics problems strengthens understanding of counting techniques.

Browse courses on Combinatorics

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Find practice problems on combinatorics
Attempt to solve the problems
Review solutions to understand the correct approach

Participate in weekly study group discussions

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Regular discussions foster a deeper understanding through peer collaboration and problem-solving.

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Join or form a study group with classmates
Meet regularly to discuss course topics and assignments
Collaborate on solving problems and understanding concepts

Create a mind map of graph theory concepts

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Creating a mind map helps visualize and connect key concepts in graph theory.

Browse courses on Graph Theory

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Gather resources on graph theory concepts
Identify the main concepts and their relationships
Create a visual representation of the mind map

Develop a presentation on network flow algorithms

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Creating a presentation requires a comprehensive understanding and ability to explain complex algorithms.

Browse courses on Network Flows

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Research network flow algorithms
Develop a presentation outline
Create slides and visual aids
Rehearse the presentation

Career center

Learners who complete 离散数学 will develop knowledge and skills that may be useful to these careers:

Software Engineer

A Software Engineer designs, develops, and maintains software applications. They work on a variety of projects, from small personal apps to large enterprise systems. This course could be useful in providing the Software Engineer with a foundation in discrete mathematics, which is used in many aspects of software development, such as algorithm design and data structures. Understanding discrete mathematics can help the Software Engineer to design and develop more efficient and effective software.

See salaries and explore the career path for Software Engineer

Data Scientist

A Data Scientist uses statistical and mathematical methods to extract insights from data. They work on a variety of projects, from analyzing customer data to developing predictive models. This course may be useful in providing the Data Scientist with a foundation in discrete mathematics, which is used in many data science techniques, such as machine learning and data mining. Understanding discrete mathematics can help the Data Scientist to develop more accurate and reliable models.

See salaries and explore the career path for Data Scientist

Operations Research Analyst

An Operations Research Analyst uses mathematical and statistical methods to improve the efficiency of organizations. They work on a variety of projects, from scheduling production lines to routing delivery trucks. This course may be useful in providing the Operations Research Analyst with a foundation in discrete mathematics, which is used in many operations research techniques, such as linear programming and network optimization. Understanding discrete mathematics can help the Operations Research Analyst to develop more effective and efficient solutions to real-world problems.

See salaries and explore the career path for Operations Research Analyst

Statistician

A Statistician uses mathematical and statistical methods to collect, analyze, and interpret data. They work on a variety of projects, from conducting surveys to developing statistical models. This course may be useful in providing the Statistician with a foundation in discrete mathematics, which is used in many statistical techniques, such as sampling and hypothesis testing. Understanding discrete mathematics can help the Statistician to develop more accurate and reliable models for analyzing data.

See salaries and explore the career path for Statistician

Quantitative Analyst

A Quantitative Analyst uses mathematical and statistical methods to analyze financial data. They work on a variety of projects, from developing trading strategies to managing risk. This course may be useful in providing the Quantitative Analyst with a foundation in discrete mathematics, which is used in many quantitative finance techniques, such as stochastic calculus and optimization. Understanding discrete mathematics can help the Quantitative Analyst to develop more accurate and reliable models for analyzing financial data.

See salaries and explore the career path for Quantitative Analyst

Actuary

An Actuary uses mathematical and statistical methods to assess risk and uncertainty. They work on a variety of projects, from pricing insurance policies to developing investment strategies. This course may be useful in providing the Actuary with a foundation in discrete mathematics, which is used in many actuarial techniques, such as risk modeling and financial planning. Understanding discrete mathematics can help the Actuary to develop more accurate and reliable models for assessing risk and uncertainty.

See salaries and explore the career path for Actuary

Computer Scientist

A Computer Scientist researches and designs new computing technologies. They work on a variety of projects, from developing new programming languages to designing new computer architectures. This course may be useful in providing the Computer Scientist with a foundation in discrete mathematics, which is used in many areas of computer science, such as algorithm design and complexity theory. Understanding discrete mathematics can help the Computer Scientist to develop more efficient and effective algorithms and systems.

See salaries and explore the career path for Computer Scientist

Business Analyst

A Business Analyst uses mathematical and statistical methods to analyze business data. They work on a variety of projects, from developing marketing strategies to improving customer service. This course may be useful in providing the Business Analyst with a foundation in discrete mathematics, which is used in many business analysis techniques, such as data mining and forecasting. Understanding discrete mathematics can help the Business Analyst to develop more accurate and reliable models for analyzing business data.

See salaries and explore the career path for Business Analyst

Technical Writer

A Technical Writer creates and edits technical documentation, such as user manuals and white papers. This course may be useful in providing the Technical Writer with a foundation in discrete mathematics, which is used in many areas of technical writing, such as explaining complex technical concepts. Understanding discrete mathematics can help the Technical Writer to write more accurate and clear technical documentation.

See salaries and explore the career path for Technical Writer

Teacher

A Teacher develops and delivers lesson plans and teaches students in a classroom setting. This course may be useful in providing the Teacher with a foundation in discrete mathematics, which is used in many areas of mathematics education, such as teaching algebra and number theory. Understanding discrete mathematics can help the Teacher to develop more effective and engaging lesson plans.

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Math Tutor

A Math Tutor helps students learn mathematical concepts and solve math problems. This course may be useful in providing the Math Tutor with a foundation in discrete mathematics, which is used in many areas of mathematics education, such as teaching algebra and number theory. Understanding discrete mathematics can help the Math Tutor to provide more effective and targeted tutoring.

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Archivist

An Archivist collects, preserves, and provides access to historical records. This course may be useful in providing the Archivist with a foundation in discrete mathematics, which is used in many areas of archival science, such as document classification and preservation. Understanding discrete mathematics can help the Archivist to develop more effective and efficient systems for managing and preserving historical records.

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Museum curator

A Museum Curator oversees the collection and preservation of museum artifacts. This course may be useful in providing the Museum Curator with a foundation in discrete mathematics, which is used in many areas of museum studies, such as collection management and exhibition design. Understanding discrete mathematics can help the Museum Curator to develop more effective and efficient systems for managing and displaying museum collections.

See salaries and explore the career path for Museum curator

Librarian

A Librarian organizes and maintains library collections and assists patrons with finding information. This course may be useful in providing the Librarian with a foundation in discrete mathematics, which is used in many areas of library science, such as cataloging and classification. Understanding discrete mathematics can help the Librarian to develop more efficient and effective systems for organizing and managing library collections.

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Data Entry Clerk

A Data Entry Clerk enters data into a computer system. This course may be useful in providing the Data Entry Clerk with a foundation in discrete mathematics, which is used in many areas of data entry, such as data validation and error correction. Understanding discrete mathematics can help the Data Entry Clerk to develop more accurate and efficient methods for entering data into a computer system.

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Reading list

We've selected 14 books that we think will supplement your learning. Use these to develop background knowledge, enrich your coursework, and gain a deeper understanding of the topics covered in 离散数学.

The Mathematical Theory of Communication

Save

Classic introduction to discrete mathematics, covering a wide range of topics from set theory to graph theory. It valuable resource for anyone who wants to learn more about the foundations of computer science.

(English) The Mathematical Theory of Communication

Paperback

(English) The Mathematical Theory of Communication

Kindle Edition

Concrete Mathematics

Save

Classic textbook on discrete mathematics, covering a wide range of topics from set theory to graph theory. It valuable resource for anyone who wants to learn more about the foundations of computer science.

(English) Concrete Mathematics: A Foundation for Computer...

Kindle Edition

$$$

Discrete Mathematics and Its Applications

Save

Comprehensive introduction to discrete mathematics, covering a wide range of topics from logic to graph theory. It valuable resource for anyone who wants to learn more about the foundations of computer science.

(English) Discrete Mathematics and Its Applications

Paperback

$$$

(English) Discrete Mathematics and Its Applications

Hardcover

$$$$

(English) Student's Solutions Guide for Discrete Mathematics...

Paperback

$$$$

(English) Connect Access Card for Discrete Mathematics and...

Printed Access Code