Foundations Pure maths for physics undergrads

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Starting a physics degree with a focus on theoretical research necessitates a solid foundation in pure mathematics. While the physics curriculum will cover essential mathematical applications, enhancing skills in areas such as analysis, pure algebra, and calculus is crucial. Recommended first-year books for self-study in these topics include those that provide a strong theoretical background and practical problem-solving techniques. Engaging with these resources will prepare students for the mathematical challenges encountered in advanced physics studies and research.
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I am off to start a physics degree in September, with the aim of going into theoretical research. However, for this I feel my pure maths skills need to be better. I know in a physics degree I will learn how to use pure maths (how to solve differential equation, how to use matrices, how to use geometry) however I would also like to know some pure maths (analysis, pure algebra, pure calculus etc). What are good first year books on these topics?
 
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