Discrete Structures: Worth Studying for Maths Majors?

[qspeechc]

Hi. I would be terribly grateful for your help. I am a second year student, and I am pretty sure I will major in Mathematics, and will probably (if I'm smart enough), do maths post-grad.
I was looking through the faculty handbook, and saw that for 2nd year math they offered a module on Discrete Structures. On the Information sheet they describe it as generally useful for mathematics. Unfortunately, I am just not able to fit this module on to my time-table, and so cannot take it.
The description they give is:

DISCRETE STRUCTURES: Introduction to informal logic; use of truthtables, quantifiers. Methods of proof (contradiction, induction). Informal set theory, relations, equivalences, partitions, partial orders. Boolean algebras. Functions, cardinality. Recurrence relations. Introduction to graph theory.

It is not a required module to major in mathematics, but from what I understand, this is important stuff.
Is Discrete Structures worth studying in my own time? If so, what textbooks would you recommend?
Thank-you.

 

[TonyG]

Hello,

Thank you for reaching out for help with your decision about taking the Discrete Structures module. I can definitely appreciate your desire to make the most informed decision about your academic path.

First of all, I want to assure you that Discrete Structures is indeed an important topic in mathematics and has applications in many fields such as computer science, cryptography, and operations research. It provides a foundation for understanding and analyzing discrete objects, which are typically encountered in real-world problems.

While the module may not be required for your major, it is definitely worth studying in your own time if you have a strong interest in mathematics and its applications. The concepts covered in the module, such as logic, proof methods, set theory, and graph theory, are fundamental and will be beneficial for your future studies in mathematics and related fields.

As for textbooks, there are many good options available depending on your level of understanding and preferred learning style. Some popular choices include "Discrete Mathematics and Its Applications" by Kenneth Rosen, "Discrete Mathematics: Elementary and Beyond" by László Lovász, and "Concrete Mathematics: A Foundation for Computer Science" by Ronald Graham, Donald Knuth, and Oren Patashnik. I recommend browsing through these and other options to find the one that best suits your needs.

In conclusion, I believe that studying Discrete Structures would be a valuable addition to your academic journey in mathematics. However, if it is not possible for you to take the module now, I would encourage you to explore the topic on your own time and perhaps consider taking it in the future if it aligns with your academic goals.

Best of luck in your studies!

 

[Mene]

Hi there. I can definitely attest to the importance of studying Discrete Structures for mathematics majors. Discrete Structures is a fundamental area of mathematics that deals with discrete objects, such as integers, graphs, and logic. It is used extensively in many fields of science, including computer science, engineering, and statistics. In fact, many real-world problems can be represented and solved using discrete structures.

Moreover, Discrete Structures is a prerequisite for many advanced courses in mathematics, including combinatorics, number theory, and cryptography. So, if you are planning on pursuing a post-graduate degree in mathematics, it would definitely be beneficial to have a solid understanding of Discrete Structures.

Although it may not be a required module for your major, I would highly recommend studying it in your own time if you have the opportunity. There are many great textbooks available on the subject, such as "Discrete Mathematics and Its Applications" by Kenneth H. Rosen and "Discrete Mathematics" by Richard Johnsonbaugh. You could also find online resources and practice problems to supplement your learning.

In summary, Discrete Structures is definitely worth studying for mathematics majors. It will not only enhance your understanding of fundamental mathematical concepts, but also provide a strong foundation for future studies and career opportunities. I wish you all the best in your academic journey!