Spring 2021 - MATH 242 D100
Introduction to Analysis I (3)
Class Number: 3554
Delivery Method: Remote
Course Times + Location:
Mo, We, Fr 1:30 PM – 2:20 PM
REMOTE LEARNING, Burnaby
Exam Times + Location:
Apr 21, 2021
12:00 PM – 3:00 PM
REMOTE LEARNING, Burnaby
Prerequisites:MATH 152; or MATH 155 or 158 with a grade of B.
Mathematical induction. Limits of real sequences and real functions. Continuity and its consequences. The mean value theorem. The fundamental theorem of calculus. Series. Quantitative.
This course will be delivered online. You are expected to have access to a reliable internet connection. You will need a computer from which you can download course materials and activities and watch live and/or recorded lectures and participate in live tutorials or workshops.
You will need a camera to take photographs of your work. A phone is acceptable.
Week 1: Techniques of Proof II §1.4, Basic Set Operations, §2.1
Week 2: Relations, Functions, Cardinality, Axioms for Set Theory §2.2– 2.5
Week 3: Ordered Fields [Absolute Value] §3.2, Completeness Axiom [Density]
Week 4: Topology of the Real Numbers §3.3–3.4, Convergence, Limit Theorems, Monotone and Cauchy sequences, §4.1–4.3, Quiz I
Week 5: Subsequences [limsup an liminf] §4.4, Compact Sets [Heine-Borel, Bolzano-Weierstrass] §3.5
Week 6: Limits of functions, Continuity and properties §5.1–5.3
Week 7: Midterm, Uniform continuity §5.4
Week 8: Derivative, Mean Value Theorem, L'Hospital's Rule, Taylor's Theorem §6.1–6.4
Week 9: Riemann integral, Properties of the Riemann Integral, Fundamental Theorem of Calculus §7.1–7.3
Week 10: Convergence of series, Convergence tests, Power Series §8.1–8.3, Quiz II
Week 11: 11 Nov = Remembrance Day (tutorials cancelled), Uniform convergence §9.1
Week 12: Applications of Uniform Convergence, Uniform Convergence of Power series [Abel's Theorem, Fourier Series examples] §9.2–9.3
Week 13: [time allocation for quizzes]
Week 14: Review
- Lecture: synchronous- lectures will be held at fixed times, on-line
- Midterm(s): synchronous; date: TBA
- Final exam: synchronous; date: TBA
- Homework (11) (best 10 each worth 2%) 20%
- Midterm 1 20%
- Midterm 2 20%
- Final Exam 40%
THE INSTRUCTOR RESERVES THE RIGHT TO CHANGE ANY OF THE ABOVE INFORMATION.
Students should be aware that they have certain rights to confidentiality concerning the return of course papers and the posting of marks.
Please pay careful attention to the options discussed in class at the beginning of the semester.
Analysis with an Introduction to Proof
Steven R Lay
ACADEMIC INTEGRITY: YOUR WORK, YOUR SUCCESS
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TEACHING AT SFU IN SPRING 2021
Teaching at SFU in spring 2021 will be conducted primarily through remote methods. There will be in-person course components in a few exceptional cases where this is fundamental to the educational goals of the course. Such course components will be clearly identified at registration, as will course components that will be “live” (synchronous) vs. at your own pace (asynchronous). Enrollment acknowledges that remote study may entail different modes of learning, interaction with your instructor, and ways of getting feedback on your work than may be the case for in-person classes. To ensure you can access all course materials, we recommend you have access to a computer with a microphone and camera, and the internet. In some cases your instructor may use Zoom or other means requiring a camera and microphone to invigilate exams. If proctoring software will be used, this will be confirmed in the first week of class.Students with hidden or visible disabilities who believe they may need class or exam accommodations, including in the current context of remote learning, are encouraged to register with the SFU Centre for Accessible Learning (email@example.com or 778-782-3112).