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In summary, the conversation discusses the difficulty in finding good books on writing proofs and other math topics outside of the curriculum for an ME major. The speaker has purchased a book on writing proofs but lacks solutions for the exercises and is seeking feedback since they are self-taught. They also mention looking for good books on PDEs, analysis, and complex analysis. Other participants in the conversation recommend looking into Springer Undergraduate Mathematics Series, which have solutions for all exercises, but some versions may not have solutions. It is suggested to check the Table of Contents before purchasing to ensure a solutions section is included.

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Bingo said:

I learned how to write proofs while reading an "easier" kind of Topology textbook. A lot of people are intimidated and never take Topology, but there really is nothing to fear. You're dealing with sets basically. It will help with Analysis as well.

Anyways, they have many simple proof problems anyone can solve. It helped me build the logic and such required to write a proof. It's not all about deducing, but knowing what's concrete and such.

Also, Analysis has a lot of proofs too, but I'm not aware of any having solutions at the back of the book though. So, I don't know what to say there.

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Springer have a series of accessible undergrad books (Springer Undergraduate Mathematics Series, or SUMS) with answers to all the exercises. My recommendation is to see if your school's library has copies on hand, or look for used ones. Although new copies aren't as expensive as most textbooks.

In fact, http://www.springer.com/west/home/math/algebra?SGWID=4-10043-580-173622659-DISPLAY_TYPE=DISPLAY_TYPE_TITLES&RESULTS_PER_PAGE=10&resultStart=0 [Broken] is the list of all books in that series.

In fact, http://www.springer.com/west/home/math/algebra?SGWID=4-10043-580-173622659-DISPLAY_TYPE=DISPLAY_TYPE_TITLES&RESULTS_PER_PAGE=10&resultStart=0 [Broken] is the list of all books in that series.

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morphism said:

In fact, http://www.springer.com/west/home/math/algebra?SGWID=4-10043-580-173622659-DISPLAY_TYPE=DISPLAY_TYPE_TITLES&RESULTS_PER_PAGE=10&resultStart=0 [Broken] is the list of all books in that series.

I have a textbook from them and have seen others and don't have solutions whatsoever.

Different version maybe?

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I recommend reading the Table of Contents to make sure there is a solutions section before buying it.

Some popular books for self-teaching in science include "A Brief History of Time" by Stephen Hawking, "The Selfish Gene" by Richard Dawkins, "The Origin of Species" by Charles Darwin, "The Elegant Universe" by Brian Greene, and "Sapiens: A Brief History of Humankind" by Yuval Noah Harari.

While these books provide valuable knowledge and insights, they cannot completely replace a formal education in science. They can serve as a supplement to formal education, but it is important to also have hands-on experience and guidance from qualified instructors.

These books vary in their level of complexity, but many of them are written in a way that can be understood by readers with little to no prior knowledge in science. However, some may require a basic understanding of scientific concepts.

Yes, in addition to these books, there are other resources that can help with self-learning in science. Online courses, scientific articles and journals, and educational videos are all great tools to supplement your learning.

While these books cover a variety of topics in science, they may not cover all branches in depth. It is important to choose books that align with your specific interests and goals in science. There may also be other resources that are more specialized in certain branches of science.

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