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<!-- Thursday: Using continuity of a function to decide the limit of a sequence Dangers of exchanging limits (prove nothing, just show that there is something to consider here) Power series definition Power series absolute convergence Power series radius of convergence Power series convergence at its radius Term by term derivative of a power series (state theorem and apply it; no proof) Show the resulting power series might not be convergent at the boundary Taylor series as power series Application of Taylor series Friday: NO FRIDAY LECTURE --> ## MATH2340 & MATH2350 #### 2025 Lectures: 3 hours, Workshops: 1 hour, Weeks: 13 <!-- .slide: class="smallertext" data-auto-animate data-auto-animate-restart --> --- ## MATH2340 & MATH2350 #### 2025 Lectures: 3 hours, Workshops: 1 hour, Weeks: 13 #### 2026 approved Lectures: 2 hours, Workshops: 2 hours, Weeks: 12 <!-- .slide: class="smallertext" data-auto-animate --> --- ## MATH2340 & MATH2350 #### 2025 Lectures: 3 hours, Workshops: 1 hour, Weeks: 13 #### 2026 approved Lectures: 2 hours, Workshops: 2 hours, Weeks: 12 #### 2026 proposal Lectures: 0 hours, Workshops: 4 hours, Weeks: 12. Lectures would still exist, but they would be prerecorded and available on Canvas. <!-- .slide: class="smallertext" data-auto-animate --> --- ## MATH2340 & MATH2350 #### 2026 proposal Lectures: 0 hours, Workshops: 4 hours, Weeks: 12. Lectures would still exist, but they would be prerecorded and available on Canvas. Purpose: * Students spend too little time *doing* mathematics, too much time passively listening. * Fully flipped models of instruction have been very successful for teaching proof based mathematics courses. See eg studies from UMich. * Tools exist for automatically grading active reading of preparatory text / active watching of recorded lectures. See eg. Perusall. * Efficiency: lectures need not change in subsequent offerings. <!-- .slide: class="smallertext" data-auto-animate --> --- ## MATH2340 & MATH2350 #### 2026 proposal Lectures: 0 hours, Workshops: 4 hours, Weeks: 12. Lectures would still exist, but they would be prerecorded and available on Canvas. But the extra 2 hours of workshop could be labelled as "lecture", and could be as a single group of approx 50 students instead of parallel sections. 1. How does this interact with required recording of lectures? 1. How does this interact with staffing hours (in 2026 / in future years)? 1. How does this affect future instructors of the same courses? <!-- .slide: class="smallertext" data-auto-animate --> --- ## MATH2340 & MATH2350 #### An orthogonal proposal Can we rearrange so that one course is *Linear Algebra*, and the other is *Introduction to Real Analysis*? <!-- .slide: class="smallertext" data-auto-animate -->