Algebra Seeking the Recommendation on Complexity Theory

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The discussion centers on a college junior majoring in mathematics who is seeking guidance on resources related to complexity theory, particularly in the context of algebraic computation, approximation, and measure theory. The individual is looking for both introductory and comprehensive books that cover these topics in depth. The request emphasizes the need for literature that aligns with their research project in theoretical computing, highlighting an interest in foundational and advanced materials in complexity theory.
bacte2013
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Dear Physics Forum personnel,

I am a rising college junior in US with a major in mathematics and an aspiring applied mathematician in the fields of theoretical computing. I just recently got a research project on the complexity theory about the algebraic computation, approximation, and measure theory. I am curious if there is both introductory and comprehensive books on the complexity theory with specific focus on my area. Could you guide me?
 
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