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Schaum's Outline of Mathematics of Finance, by Petr Zima and Robert L. Brown (will contain the crucial mathematics of finance that you would find useful for investments, mortgages, debt finance, etc.; you should be able to do most if not all of the maths in a finance degree with this book alone)
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Mathematics for Economics and Business by Ian Jacques (maths you would need for economics or business/finance - good book if you haven't done further maths but done at least A Level Maths)
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Schaum's Outline of Introduction to Mathematical Economics by Dowling, Edward (good introductory book on how to apply A Level Maths in economics; will be useful if you decide to pick Mathematical Economics modules, which are usually challenging; if you want to see how the maths is applied in economics, then this is a good book to start from)
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A Random Walk Down Wall Street: The Time-Tested Strategy for Successful Investing by Burton Malkiel (classic reading for finance)
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Pretty much any textbook by Gregory Mankiw (good introductory books on economics; he's a good author, and probably a favourite of economics students; I would hold back on buying one until your first and second years because they might be essential text for your degree)
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Basic Econometrics by Damodar N. Gujarati (this is my go to for econometrics/statistics for economics; it should be an essential text for your degree, but if it's not, it's definitely a go to)
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The Freakanomics series by Stephen J. Dubner and Steven Levitt (it's a fun application of economics in unusual circumstances; I wouldn't use the information to quote in your assignments and essays though)
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The Undercover Economist by Tim Harford (another fun book on seeing economics in different circumstances, but more conventional than Freakanomics)
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Corporate Finance: Principles and Practice by Anthony Head and Denzil Watson (my favourite textbook on corporate finance; most finance textbooks can be long and very very dry. This is a fun read; recommend looking in this book if you have finance modules in your degree)
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Books by Peter Lynch and Mary Buffett - for an alternative in investment philosophy and approach
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The Intelligent Investor by Benjamin Graham (a classic text for finance, and the mentor of Warren Buffett - most of the information is out of date though according to a number of authors, but some of the principles are still good)
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Books by Michael Lewis and Jordan Belfort - for insight into the finance industry and things you shouldn't do
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