Top Math Books for Self-Study: 1st Year University Course | NSW, Australia

[Mentallic]

I'm just out of high school and will be starting an advanced mathematics course in University (NSW, Australia). I'm unsure what each course consists of specifically, and all I've really heard about that will be in it is "discrete mathematics".
It's vital that I get good marks on average throughout the first year, so I thought I would start early with self-study.

What book(s) do you guys recommend? Note I took extension 2 mathematics in high school (the highest level available) so I'm already proficient in quite a few topics such as single-variable calculus, trigonometry, complex numbers, polynomials etc.

Thanks in advance for any suggestions.

 

[ojs]

I suggest you read the wikipedia entry http://en.wikipedia.org/wiki/Discrete_mathematics and have a look at the section at the bottom named Further reading, the book by Norman L. Biggs mentioned first seems to be ok.

 

[charng]

I understand the importance of self-study and preparation in any field of study, especially in mathematics. Congratulations on taking the initiative to start early and improve your understanding of the subject.

Firstly, I would recommend familiarizing yourself with the specific curriculum and topics covered in the first year mathematics course at your university. This will give you a better idea of what to expect and what areas you may need to focus on.

In terms of books, there are many great resources available for self-study in mathematics. Some popular options for first-year university courses include "Calculus: Early Transcendentals" by James Stewart, "Discrete Mathematics and Its Applications" by Kenneth Rosen, and "Linear Algebra and Its Applications" by David Lay. These books cover a wide range of topics and are often used as textbooks in university courses.

Since you have already mastered some topics in high school, you may also want to consider more advanced texts such as "Advanced Engineering Mathematics" by Erwin Kreyszig or "Real Analysis" by Royden and Fitzpatrick. These books may challenge you further and provide a deeper understanding of the subject.

Additionally, I would recommend utilizing online resources such as Khan Academy, MIT OpenCourseWare, and Coursera courses to supplement your self-study. These platforms offer a variety of resources, including video lectures, practice problems, and interactive quizzes.

In conclusion, it is important to choose a book that aligns with your learning style and covers the topics included in your university course. Don't be afraid to reach out to your professors or peers for recommendations and additional resources. With dedication and hard work, I am confident you will excel in your first year mathematics course. Best of luck!