Advanced Precalculus: Geometry, Trigonometry and Exponentials

A very good course which I found, personally, difficult and demanding. A lot of fellow students appeared to have strong mathematical backgrounds and were probably familiar with many of the topics covered. I found a tendency for the videos to speak maths rather than teach it although Carlo and Alberto’s videos of the answers to the questions were much better in this respect. Of course, they were after spending a lot of time tackling the questions. I found it a huge leap from Francis’ introductory videos to the nature of the questions. For me, a few intermediate stepping stones would have been welcome. Almost invariably, I found the need to consult other texts to learn and understand the topics. That’s a fair and reasonable approach to learning but it would be misleading for a prospective student to believe this was a self-contained course. Spending 5 to 6 hours a week was, for me, a gross underestimate of the time that was required to study. It took me between 25 to 30 hours but I appreciate that indicating this as a requirement would turn a lot of students away. It would be interesting to know how much time the more mathematical experienced students took. There were quite a few errors in the text material and the Educators were prompt to respond. However, the course material needs to be checked before the next run of the course. Also, the typographical set often created ambiguity and needs to be addressed. I remember the companion course started by inviting students to state their view of mathematics and mathematicians and I think it was clear that the Course Team were anxious to dispel the image of mathematicians being nerds. I welcome that view because it is probably the biggest single factor that turns people away from mathematics. Unfortunately, many of the introductory videos in this (second) course actively promoted the nerd image - a great shame! A second run of the course would benefit by having dedicated comments and discussion sections associated with the quizzes,

This and the earlier precalculus course from the University of Padova are two of the best courses on FutureLearn, both challenging but enjoyable. They have a regular structure, the theory of each topic is discussed followed by practical examples of problem solving based on the theory, then the student is provided by a quiz to test their understanding. At the end of each week there’s an optional test. The final week includes a test covering all course topics.

Three things demonstrated to me the high quality of the course development:
- The student is obliged to make their own notes, just copying the course text and downloading the videos and pdfs is insufficient when faced with quiz and test questions. This ensures that the topic is learnt.
- The courses are progressive. topics often call on the knowledge gained earlier which is a great way of learning. It also provides a check for the student that they have understood sufficient of the previous content.
- The questions are designed to make you think. The worked examples illustrate the techniques but don’t provided complete model answers for quiz and test questions. These are only provided once the question has been answered.

10/10

Very enjoyable. All the tutors are knowledgable, enthusiastic and engaging. The structure of the course, with a lecture followed by worked examples which you are encouraged to try yourself, works really well.
The pace is quite fast and some of the material is challenging (it was for me anyway) but everything is explained well and if you go back and look at the lecture or the pdf that accompanies it you will find what you are looking for.
I have studied a quite a bit of maths over the years but there was still lots here that was new to me; or explained in ways that gave a fresh insight. The delivery was entertaining and often amusing.
The educators engaged in discussions with the learners, and any errors were quickly corrected. My favourite MOOC so far!

Very demanding zciriculum and fun, and serious concentration is needed,. Was a little tool fast to take in 8-10 minutes per section of the course though, I had to play it some time more than once to capture all of the technical information and answers and draw all the appropriate graphs to accompany the formulas on there different axis and all the reflection index on their axis and naturally draw all the area space to calculate their surface area and internal areas then sum up the total area with illustrations so that the next time things will be easier. I think for me I will do this again to make sure I have the right knowledge, but I have 2 medical examination to take from Bath University to complete the course with Bath University and after I will return to Maths. Thank you Padova University for the course and all the best for the future years.