Math Degree: Bridging the Gap and Understanding Calculus

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    Degree Mathematics
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Discussion Overview

The discussion centers on the challenges faced by participants transitioning from basic calculus to higher-level mathematics, particularly in understanding proofs and abstract concepts. Participants seek recommendations for resources to strengthen their mathematical foundations.

Discussion Character

  • Exploratory, Homework-related

Main Points Raised

  • One participant expresses a feeling of inadequacy in their mathematical understanding despite completing calculus and differential equations, indicating a desire to understand the underlying principles.
  • Another participant suggests engaging with proofs and seeking help from professors when difficulties arise.
  • A participant mentions considering "Bridge to Abstract Mathematics" by Morash for self-study but is uncertain about its suitability.
  • Another participant recommends "An Introduction To Mathematical Reasoning" by Peter Eccles as a helpful resource.
  • One participant agrees with the choice of Morash's book, recalling that it includes sections on writing formal proofs relevant to students with a calculus background.
  • A different participant recommends "Reading, Writing, and Proving" by Daepp and Gorkin, and "A Transition to Advanced Mathematics" by Smith, Eggen, and St. Andre, while also mentioning "Set Theory and Metric Spaces" by Irving Kaplansky as a valuable introduction to abstract mathematics.

Areas of Agreement / Disagreement

Participants generally agree on the need for additional resources and strategies to bridge gaps in understanding, but there is no consensus on a single best approach or resource.

Contextual Notes

Participants express varying levels of confidence in their mathematical backgrounds and the resources they are considering, indicating that personal experiences and preferences may influence their choices.

Who May Find This Useful

Students transitioning to higher-level mathematics, particularly those seeking to strengthen their understanding of proofs and abstract concepts.

bonfire09
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Well I've taken calculus 1-3 all up to differential equations and its been quite easy. Though I forgot most of the stuff already. I am going to be taking upper division math but I feel that my math background is still very weak because all I ever did was computations.I never understood why It works. I mean I tried to prove it but I never got it. I know that I have gaps. Anyone recommend any books or what should I do to close these gaps?
 
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maybe try and do the proofs and when you get stuck talk to your professor
 
yeah I tried. I am thinking of using a book called Bridge to Abstract Mathematics by Morash as a guide for self study but idk if I am on the right track.
 
I like An Introduction To Mathematical Reasoning by Peter Eccles.
 
bonfire09 said:
yeah I tried. I am thinking of using a book called Bridge to Abstract Mathematics by Morash as a guide for self study but idk if I am on the right track.

Looks like the right track to me. I think I might even seen this book before...from what I remember it had sections on how to write formal proofs by proving basic concepts a student having only encountered calculus might recognize.
 
I recommend "Reading, Writing, and Proving" by Daepp and Gorkin, and "A Transition to Advanced Mathematics" by Smith, Eggen, and St. Andre. Though not as general, "Set Theory and Metric Spaces" by Irving Kaplansky is a beautiful little book that was my first exposure to abstract mathematics.
 

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