<p>After poking around in the web sites of the math depts at UW, Caltech, MIT and a number of other schools, I found some answers to my questions about rigor of university intro calculus courses and thought I would share my findings in case others are trying to choose a math course path.</p>
<p>What I found from looking at past exams and homework is that UW Math 124 and 124H appear very similar – same textbook, cover the same material, except the 124H section has smaller classes and some slightly harder problems.</p>
<p>There is a much bigger difference between 124 and 134. Whereas math 124 focuses on practical problem-solving, much like AP Calc BC, math 134 offers a more conceptual approach to math, with more rigor, a harder textbook, Salas, and requires proofs rather than mere solutions to problems. Proofs in mathematics will be a new concept to most high schoolers, but this approach leads to a deeper level of understanding of the concepts in calculus as opposed to merely applying formulas. Another difference between 124 and 134 is that 134 is accelerated and the pace it goes at is likely to make it even more difficult than the rigor of the material. The math 134 professor’s syllabus states that you should take this course only if you already have a very solid foundation in calculus.</p>
<p>Now, to compare UW math courses to other universities, I looked at past exams and problem sets at some really tough schools: MIT, Caltech, U. Chicago, and University of Toronto. </p>
<p>Caltech requires all incoming freshman, regardless of major, to take a rigorous, proof-based calculus course using a textbook, Apostol, that is harder (more theoretical) than the one used in UW 134. </p>
<p>MIT has a range of intro calculus courses all a bit harder, but basically similar to UW. In general, only theoretical math majors tend to take the proof-based intro calc course at MIT, which is very similar to (same textbook as) Caltech calculus. But the other intro calc options at MIT are not proof-based.</p>
<p>U. Chicago and University of Toronto both have courses that use the same textbook (Salas) as UW math 134, and at these schools, this proof-based course is designed for all science majors. These two schools have an even harder course for the hardcore math students that is more theoretical – uses Spivak as textbook, which is similar in rigor to the Apostol text used at Caltech and MIT.</p>
<p>So, bottom line, based on the textbook and exams, UW math 134 looks like a great course for anyone wanting a solid, rigorous math foundation with a good balance of theory and practice, much harder than 124 but not so theoretical that it is only useful for math majors.</p>