readingList

Please forgive me for being long-winded since every book here has kept a memory of my story.

Mathematics:

Books I read:

• Calculus by James Stewart

I am sure that this is one of the most famous calculus books in the world.

• Thomas's Calculus by George B. Thomas

I refered more on this book when I was learning the multiple integrals part, compared to the one written by James Stewart.

• Vector Calculus by Matthews, Paul C.

It was my primary reference book for my second year and the author Paul is from our school. This book is so fantastic that my notes on this book even cover the whole texts!

• Advanced Engineering Mathematics by Erwin Kreyszig

This books gave me a good start of learning Differential equations from my first year in the unviersity, now it was more like a tool book for me to refer some concepts I learnt quickly. However, I haven't read the part E, F, G.

• Nonlinear dynamics and Chaos by Steven H. Strogatz

It is this book that brings me to the nonlinear beauty of this world. Steven has another book called 'Infinite powers', which makes me know the how powful calculus is.

• Differential Equations, Dynamical Systems, and an Introduction to Chaos by Morris/Stephen/Robert

I still remember that I use this book to teach myself about nonlinear dynamics and the end of 2020. I've gained a basic roadmap of learning dynamical system for my further study because of this book. It is also this book that make me to choose course Mathematical Biology and Medicine for my final year study due to the Hodgkin-Huxley model in this book.

• Complex Variables and Application by James Ward Brown and Ruel V.Churchill

This book is mainly used as an exercise book for me to practice the skills like Taylor series and Residues theorem. Excellent example in this book, isn't it? This book's hard cover has been destroyed due to a serious fire accident happend in my house. I could still remember that I chose to go back to my room, which was coverd by fire and smoke, to take this book with me out even though I escaped from the fire successfully at the first time.

• Elementary Differential Equations and Boundary Value Problems by Boyce/Diprima/Meade

This is my primary reference book when I was learning the course Differential equation and fouier analysis. I learnt lots of advanced skills for applied mathematics. This book saved my life when I was quite struggling with the solution of Bessel's equations and legrendre's equation.

• Introduction to Linear Algebra by Gilbert Strang

I took the corresponding online open courses when I was learning the linear algebra. Gilbert's new way to start linear algebra is quite attractive. I also read serveval chapters of his book Differential Equations with Linear Algebra.

• A First Course in Probability by Sheldon Ross

It is the 'first reference book' for me about probability. This book also gave me a pre-looking about the probability generating function when I was in the first year.

• Probability and Statistics by Degroot/Schervish

I mainly use Sheldon's book as knowledge learning and this book for exercise.

• Statistiacal Inference by George Casella/Roger L. Berger

When I was in the second year, I rarely use the book written by Sheldon, but this one instead. This book did boarden my horizens of statistics when I was learning the course Statistical Model and Method. I refered more on Chapters about point estimation, hypothesis testing, interval estimation, mainly focusing on the rigourous mathematical derivations, which is actually the biggest advantage of this book. This is also a book with lots of my personal notes.

• Principles of Mathematical Analysis by Walter Rudin

One of the most classical books of analysis, perhaps the best book for beginner (Chapter 1, 3, 4, 5).

• Mathematical Analysis by Apostol

This book helps me a lot when I was learning the Basic topology. Because of this book, I gradually understand the Completeness of the real numbers with six famous theorems:

1. Bolzano–Weierstrass theorem
2. Monotone convergence theorem
3. Nested intervals theorem
4. Cauchy completeness
5. Least upper bound property
6. Heine–Borel theorem

• Numerical Analysis by Richard L. Burden/Douglas J. Faires/ Annette M. Burden

It is the primary reference book when I was learning the scientific computing. However, I don't think that this book gives a good introduction to interpolation, since for beginners, it is easy to get confused about the interpolation and fitting, the difference should be emphasized.

• Advanced Mathematical Methods for Scientists and Engineers by Bender/ Orszag

Chapters about asymptotic skills for algebra, boundary layer theory, WKBJ theory, and multiple scales methods are the auxiliary materials for my study of the course Differential Equations.

Books I plan to read:

• All the mathematics you missed by Thomas A. Garrity

Since I plan to continue studying applied mathematics for my master degree, this book would be a good summary for my bachelor life. Every chapter looks quite inspiring and I actually found something I missed in my undergraduate when I was browsing. Last, the classification of the topics in this book is a good end for my mathematics life as an undergraduate.

• Nonlinear Science, the challenge of complex systems by Zensho Yoshida

I am always attracted by the nonliear beauty of this world. I think that in order to study the nonlinear world, people should have a general view of a system, but not just focus on a particular things in the system. Nonliear dynamics has brought me to the field of complex systems, which is also a field I would like to devote myself to study. I believe that this book will give me a nice guidance for my future study.

• Linear and Nonlinear Functional Analysis with Applications by Philppe G. Ciarlet

My basic goal is to finish reading the linear part of this book since this books is the most informative one of the many functional analysis books, up to 800 pages.