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离散数学

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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Syllabus

离散数学基础

组合计数

函数估计

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Read about what's good

what should give you pause

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

离散数学：理论与应用基础

根据学生们说，上海交通大学的这门离散数学课程提供了扎实且全面的基础知识基础扎实且全面，尤其适合计算机科学及相关专业的学习者。许多评论者称赞课程的讲解清晰易懂讲解清晰易懂，认为老师能够将复杂的概念讲得明白。课程内容覆盖广泛覆盖广泛，为后续的数据结构、算法等课程打下了坚实的基础。但也有学生提到，课程的作业难度较高作业难度较高，需要投入较多时间和精力，且认为课程节奏较快节奏较快，对学习者的数学基础有一定要求数学基础有一定要求。总体而言，这是一门理论性强且价值很高理论性强且价值很高的基础课程，学习投入较大学习投入较大但回报丰厚。

为计算机科学后续课程打下坚实基础。

"这门课为我后续学习数据结构和算法提供了坚实的基础。"

"课程内容非常全面，基本涵盖了离散数学在计算机科学中需要的所有基础知识。"

"我觉得这门课把基础讲得很牢固，让我对很多计算机概念有了更深的理解。"

"如果你是计算机专业的学生，这门课是非常重要的基础课，值得认真学习。"

讲师能够将复杂概念讲得明白，易于理解。

"老师的讲解非常清晰，即使是 어려운 개념도 쉽게 설명해주십니다."

"我觉得老师讲得很好，逻辑很清楚，枯燥的内容也能讲得有意思。"

"课程最大的优点就是讲师的讲解，真的能把离散数学讲明白，我学得很轻松。"

"老师的讲解深入浅出，让我对离散数学有了系统的认识。"

内容密度大，需要紧跟学习进度。

"课程讲得很快，知识点很多，感觉一不留神就跟不上了。"

"我觉得节奏有点快，如果不是每天学习，很容易落下。"

"内容很丰富，但也意味着学习强度比较大，需要自己合理安排时间。"

对数学基础要求较高，特别是逻辑和抽象思维。

"这门课对逻辑思维和数学基础要求挺高，如果数学不好可能会有点吃力。"

"我觉得有一定的数学基础会学得更顺利，尤其是一些证明题。"

"课程本身就是数学，需要你有接受抽象概念的能力。"

部分作业有挑战性，需要花费较多时间。

"作业真的有点难，有好几次我花了很长时间才做出来。"

"课程本身不难，但作业的难度比我想象的要高，需要多花点心思。"

"如果你想拿高分，作业部分不能掉以轻心，非常有挑战性。"

"我感觉作业的设计很好，虽然难，但能帮助我巩固知识点。"

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

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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

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

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

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.

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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

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.

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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

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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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.

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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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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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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

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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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

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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.

离散数学

Here's a deal for you

What's inside

Syllabus

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Save this course

Reviews summary

离散数学：理论与应用基础

Activities

Career center

Reading list

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