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Old 2021-09-09, 09:50   #32
Nick's Avatar
Dec 2012
The Netherlands

176510 Posts

Originally Posted by pinhodecarlos View Post
Ok Nick. I’m home on A/L and I’ve already packed my Piskunov books. I will re study them but I want then to think about next step. I always wanted to take a math degree but to get a job it would be better to have a engineer degree. Need to go back to my dream. Please I want your guidance.
Apologies for the late reaction: we have been away on holiday and I have only now seen your post.

University-level mathematics for mathematicians differs from mathematics for engineers or natural scientists
in its emphasis on abstraction and rigour. So alongside Piskunov it would be a good idea to read
"A Companion to Analysis" by T. W. Körner. Chapter 1 is available free here.

Similarly, you probablly have a good knowledge of linear algebra from an applied point of view, but may gain
something from a more abstract perspective. Prof. Ronald van Luijk has written his lecture notes in English
and made them freely available here, with follow-up notes by him and Michael Stoll available here.

There are various good books on the theory of groups, for example the book "Groups and Symmetry" by M. A. Armstrong.
This is where you start to get into the mathematics that engineers do not usually see!

If you are looking for a broad, accessible overview of modern pure mathematics, then the "Princeton Companion to Mathematics"
edited by Prof. Tim Gowers is worth dipping into.
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