Annotated bibliography
Book Recommendations
Five texts from a home library of over 200 books, mostly mathematics, with some geography, computer science and physics. I’m a big fan of Springer.
Recommended reading
The books that have helped me most so far, with a note on each.
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[1]
Chiossi, S. G. (2021). Essential Mathematics for Undergraduates: A Guided Approach to Algebra, Geometry, Topology and Analysis. Springer.
My main reference for MA1100T Basic Discrete Mathematics (T). It covers the course content and a good deal beyond it, in depth.
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[2]
Dummit, D. S., & Foote, R. M. (2003). Abstract Algebra (3rd ed.). Wiley.
My own algebra did not start here — I found this too abstract at the time and turned to Gallian’s Contemporary Abstract Algebra (2013), an easier text with many good examples and exercises. But one must still walk through the gates of Dummit and Foote.
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[3]
Axler, S. (2023). Linear Algebra Done Right (4th ed.). Springer.
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[4]
De Koninck, J.-M., & Luca, F. (2012). Analytic Number Theory: Exploring the Anatomy of Integers. American Mathematical Society.
The first book on analytic number theory I encountered, and the one that made me fall in love with the subject. I prefer it to the standard reference by Apostol (1976), and the exercises come with solutions. I read M. Overholt’s A Course in Analytic Number Theory (2014) alongside it; the two complement each other well.
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[5]
Johnsonbaugh, R., & Pfaffenberger, W. E. (1981). Foundations of Mathematical Analysis. Dover.
Much more readable than the usual reference, Rudin’s Principles of Mathematical Analysis. The exercises run from easy to hard and complement the exposition well. I used it for MA2108 Mathematical Analysis I. You cannot start by reading Rudin, but once you have a good grasp of real analysis it becomes manageable.