Seeking Recommendation on Discrete Mathematics textbook

[bacte2013]

Dear Physics Forum mentors,

I am an undergraduate sophomore with double majors in mathematics and microbiology. I wrote this email to seek your recommendation on the discrete mathematics textbook that is in-depth, theoretical, proof-based, and also comprehensive. I am currently taking a course in discrete mathematics and the course requires the book called "Discrete Mathematics and Its Applications" by Kenneth Rosen, but that textbook does not help me in my computational microbiology research; the research is focused on machine learning and algorithm formulation, which requires a knowledge in theoretical discrete mathematics. Although Rosen's book is very comprehensive, I do not like its explanation and a lack of in-depth presentation.

Thank you very much in advance!

PK

 

[MidgetDwarf]

Not sure about the biology aspect of your question, however Epps discrete math book is clear. Maybe you have problems writing proofs?

 

[bacte2013]

^
Thanks for the recommendation but I heard that Epp's book is more or less equivalent to Rosen's book; my computational biology is focused on machine learning and algorithm formulation, which requires a lot of theoretical knowledge from the discrete mathematics. Unfortunately, Rosen's book is not detailed enough to help me out. Does anyone used Grimaldi's Discrete and Combinatorial Mathematics? It seems quite theoretical...

 

[MidgetDwarf]

Discrete mathematics is a very broad term. It can mean anything depended on the institution. Do you need a book on combinatorics, number theory, graph etc? Most discrete mathbooks are just introduction to these mentioned math topics and others. the proofs that these books present are only a thin layer of the over a all idea of these math topics.

 

[rezeew]

:

Hello,

Thank you for reaching out to us for a recommendation on a discrete mathematics textbook. We understand that you are currently taking a course in discrete mathematics and are looking for a textbook that is in-depth, theoretical, proof-based, and comprehensive.

Based on your research focus on machine learning and algorithm formulation, we would recommend the book "Introduction to the Theory of Computation" by Michael Sipser. This textbook covers topics such as automata theory, computability, and complexity theory, which are essential for understanding algorithms and their applications in machine learning.

Additionally, if you are looking for a more comprehensive approach to discrete mathematics, we would suggest "Concrete Mathematics: A Foundation for Computer Science" by Ronald Graham, Donald Knuth, and Oren Patashnik. This textbook covers a wide range of topics in discrete mathematics, including combinatorics, graph theory, and discrete probability, which are all relevant to your research.

We hope these recommendations are helpful in your search for a suitable textbook. Best of luck in your studies and research endeavors!

Sincerely,

Physics Forum Mentor