<story><title>No-bullshit guide to linear algebra</title><url>https://gumroad.com/l/noBSLA</url></story><parent_chain><item><author>rahimnathwani</author><text>I&amp;#x27;m curious - did you work through this book on your own, or as part of a class or with help from others?&lt;p&gt;I started reading it, attempting most of the exercises at the end of each chapter, and some of the &amp;#x27;as you should verify&amp;#x27; parts.  I found the &amp;#x27;aha&amp;#x27; moments during the text or when solving the exercises really enjoyable, but I got stuck often enough that I began to only pick up the book when I felt super-alert.&lt;p&gt;I stopped about a third of the way through, a few pages before the introduction of eigenvectors and eigenvalues.  I would like to pick it up again, but am worried about how to maintain motivation the next time I&amp;#x27;m faced with a page where I&amp;#x27;m stuck&amp;#x2F;confused for 30 minutes.&lt;p&gt;EDIT: Thank you to the people who replied.  Your empathy (~&amp;quot;you&amp;#x27;re not alone in getting stuck&amp;quot;) and encouragement (~&amp;quot;you don&amp;#x27;t have to grok everything the first time through&amp;quot;) have given me new motivation to try this again.</text></item><item><author>nilkn</author><text>I always have to mention my all-time favorite introductory book on this subject:&lt;p&gt;Liner Algebra Done Right (&lt;a href=&quot;http://www.amazon.com/Linear-Algebra-Right-Undergraduate-Mathematics/dp/0387982582&quot; rel=&quot;nofollow&quot;&gt;http:&amp;#x2F;&amp;#x2F;www.amazon.com&amp;#x2F;Linear-Algebra-Right-Undergraduate-Mat...&lt;/a&gt;)&lt;p&gt;Its breakthrough is its focus on the basic algebraic properties of vector spaces and linear maps between them. It de-emphasizes matrix computations and especially determinants (they are covered, but only insomuch as they are necessary).&lt;p&gt;In my experience, the result of a typical linear algebra course is most students don&amp;#x27;t fully understand the determinant and more importantly they don&amp;#x27;t understand the proofs of major theorems which involve long manipulations of the determinant. They also don&amp;#x27;t understand the more algebraic side of the subject because they aren&amp;#x27;t given a chance to--it&amp;#x27;s not covered in much detail. The result is they don&amp;#x27;t understand the subject overall much at all.&lt;p&gt;This book is based on the observation that the abstract algebra involved in linear algebra is actually remarkably easy, much more so than arcane determinant manipulations.</text></item></parent_chain><comment><author>j2kun</author><text>Mathematicians are chronically lost and confused. It&amp;#x27;s our natural state of being, and it&amp;#x27;s okay to keep going and take what insights you can.&lt;p&gt;I suggest you don&amp;#x27;t worry too much about verifying every claim and doing every exercise before moving on. If it takes you more than 5 or 10 minutes to verify a &amp;quot;trivial&amp;quot; claim in the text, then you can accept it and move on. It&amp;#x27;s healthy, if you get stuck on such a problem, to think about other problems or come back to them later. It&amp;#x27;s not uncommon to find that by the time you revisit them you&amp;#x27;ve literally grown so much (mathematically) that they&amp;#x27;re trivial.</text></comment>
<story><title>No-bullshit guide to linear algebra</title><url>https://gumroad.com/l/noBSLA</url></story><parent_chain><item><author>rahimnathwani</author><text>I&amp;#x27;m curious - did you work through this book on your own, or as part of a class or with help from others?&lt;p&gt;I started reading it, attempting most of the exercises at the end of each chapter, and some of the &amp;#x27;as you should verify&amp;#x27; parts.  I found the &amp;#x27;aha&amp;#x27; moments during the text or when solving the exercises really enjoyable, but I got stuck often enough that I began to only pick up the book when I felt super-alert.&lt;p&gt;I stopped about a third of the way through, a few pages before the introduction of eigenvectors and eigenvalues.  I would like to pick it up again, but am worried about how to maintain motivation the next time I&amp;#x27;m faced with a page where I&amp;#x27;m stuck&amp;#x2F;confused for 30 minutes.&lt;p&gt;EDIT: Thank you to the people who replied.  Your empathy (~&amp;quot;you&amp;#x27;re not alone in getting stuck&amp;quot;) and encouragement (~&amp;quot;you don&amp;#x27;t have to grok everything the first time through&amp;quot;) have given me new motivation to try this again.</text></item><item><author>nilkn</author><text>I always have to mention my all-time favorite introductory book on this subject:&lt;p&gt;Liner Algebra Done Right (&lt;a href=&quot;http://www.amazon.com/Linear-Algebra-Right-Undergraduate-Mathematics/dp/0387982582&quot; rel=&quot;nofollow&quot;&gt;http:&amp;#x2F;&amp;#x2F;www.amazon.com&amp;#x2F;Linear-Algebra-Right-Undergraduate-Mat...&lt;/a&gt;)&lt;p&gt;Its breakthrough is its focus on the basic algebraic properties of vector spaces and linear maps between them. It de-emphasizes matrix computations and especially determinants (they are covered, but only insomuch as they are necessary).&lt;p&gt;In my experience, the result of a typical linear algebra course is most students don&amp;#x27;t fully understand the determinant and more importantly they don&amp;#x27;t understand the proofs of major theorems which involve long manipulations of the determinant. They also don&amp;#x27;t understand the more algebraic side of the subject because they aren&amp;#x27;t given a chance to--it&amp;#x27;s not covered in much detail. The result is they don&amp;#x27;t understand the subject overall much at all.&lt;p&gt;This book is based on the observation that the abstract algebra involved in linear algebra is actually remarkably easy, much more so than arcane determinant manipulations.</text></item></parent_chain><comment><author>jjoonathan</author><text>I started reading it for a class but I wasn&amp;#x27;t assigned all the problems. Later, I managed to propel myself through it by building confidence with the problems of the first few chapters (which were easy by that point) and then embracing the sunk-cost fallacy to get through the rest.&lt;p&gt;One problem stood out. I forget the chapter, but I&amp;#x27;ll never forget the problem: prove that normed vector spaces are inner product spaces IFF the parallelogram law holds. It took about half a day to crack that problem and I was completely lost for about 90% of it. (That&amp;#x27;s not a strategy. The first paragraph was my strategy. My only point here is that you aren&amp;#x27;t alone in getting stuck.)</text></comment>