This course is the second of two precalculus courses from the University of Padova, providing you with the advanced mathematical skills required to complete a first course in calculus.

You’ll get to grips with more challenging precalculus topics: plane and solid geometry; logarithms and exponentials; equalities and inequalities; and trigonometric functions and identities.

By the end of this course you’ll have gained the skills to support further mathematical studies.

This course is for anyone who wants to brush up on their basic mathematical skills, particularly students in the last year of high school, or at the beginning of undergraduate studies, who intend to take a first course in calculus.

Grahamcompleted this course, spending 25 hours a week on it and found the course difficulty to be hard.

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 bee…

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,

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!

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…

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.

One of the best Future Learn courses that I have done. I have signed up for over 40 courses so far, and this easily rates amounts the best.

The course content was comprehensive. It set its target at the correct audience. The material is challenging but provides a correct in depth discussion of the subject.

The material was presented in informative, friendly lectures which were easy to understand. This was backed up with extensive challenging exercises. The answer of these were provided in great detail.

This course provides a solid grounding for any student who is about to start learning calculus.

Very nice course, was DEFINITELY challenging b/c of the CONSTANT set theory notation. But omg, after a while it just clicked and I could understand it. I guess b/c i was exposed so long to it. Especailly compared to other courses online, I would definitely say this is prob the hardest, maybe not the MOST thorough, but its proofs are rigorous as math should be, and is definitely a taste of what REAL math is, if you know what I mean. Thank you for the great time!! and Good Luck all :D

Francis's teaching was excellent, clear easy to understand and rigorous. I found the other course tutors unclear and difficult to understand at times and although their working was correct they did seem to overcomplicate explanations and often used a slightly different notation to Francis, so I did find this a bit confusing. I am disappointed that the course has come to an end. I do hope that there will be more courses like this in future as I have really enjoyed it..

A very thorough course well presented with worked solutions to help if in difficulty.

Any comments posing questions are answered very quickly by course staff, I think they must work shifts to give such immediate responses, the most attentive monitoring of all the courses that I have done. I am just sorry that owing to other commitments I fell behind on this particular course, very rare for me not to complete a course. I shall probably sign up when it is re-run.

I appreciate a highly professional instruction, plenty of problems of varied difficulty to solve accompanied by a detailed solution of the problems both in videos and in pdf files, interesting applications of presented mathematical concepts, lots of quizes that prepare

students for the tests, the support of the educators in answering students' questions.

I love both PreCalculus and Advanced PreCalculus offered by you. My suggestion is that it will be better if Francis uses focus-directrix definition of conic section when deriving the canonical equation of ellipse, parabola, and hyperbola since it is much easier to understand. Other than that, I can safely say that this is the most impressive PreCalculus course that I have ever taken in my life.

A well designed course that is challenging, interesting and informative.

The educators explained the material well and guided learners through problems. They were ready to take part in the forum with further explanation and responded promptly to correct occasional inaccuracies

It has been a very well prepared and presented course. We covered a wide range of topics including functions, trigonometry and geometry just to mentioned a few. At the end of each topic there was a set of questions to be answered. I would strongly recommend it.

It was hard work and challenging. I didn't understand everything but by the end I felt I had learnt a great deal. It did pretty much what I hoped it would do and left me hoping that there will be another course by the same team soon.

A great deal of hard work was put into this MOOC, one of the most thorough (and demanding, but that is not a criticism) that I have done. All involved showed a love for their subject and the wish to share that. Excellent!

This course was very interesting although I feel like it had some parts that where very hard and some that where very easy (Maybe my understanding of some parts where bad and some good).

The course was perfect for me. The professors explained the material very well. I think that with so many topics the course should take a bit longer and there should be more exercises

Julicompleted this course, spending 12 hours a week on it and found the course difficulty to be medium.

The course was perfect for me. The professors explained the material very well. I think that with so many topics the course should take a bit longer and there should be more exercises.

Very clearly presented with a good standard format. Challenging but careful working through was repaid. Recommended for any novice mathematician who is keen to learn more.