Tony Croft

Tony Croft

Professor of Mathematics Education at Loughborough University specialising in mathematics for engineers and mathematics support for students who find university mathematics particularly challenging.

Location Loughborough UK


  • I did exercise 6 successfully last week. Today I tried to review what I did and simply re-run all cells again. But the

    data = read_excel('WHO POP TB some.xls')

    failed, with an error message that included the line
    XLRDError: Unsupported format, or corrupt file: Expected BOF record;

    I have struggled for a while to understand what is going wrong...

  • thank you very much John.

  • Hi. Just completed the exercise using Jupyter notebooks on SageMathCloud (
    Worked fine for me, but the File,Save option seems to be prohibited, and I couldn't find the Save and Checkpoint button.
    Close and Halt is also prohibited.
    Thanks to the team, and to anyone who has any advice about this.

  • great intro - many thanks, loved the bird and the 'right-way around' map.

  • Hi Gladys, and thanks for these final comments. I am delighted you feel inspired to take another maths course. Best wishes for the future. Tony.

  • Many thanks Allan.

  • Hi Gladys - a couple of points to make here:
    In y = mx +c, whenever m is zero the line must be horizontal because then the gradient of the line is zero. This is true whatever the value of c, including the case c=0. Recalling that c tells us where the graph cuts the vertical axis, then if c=0 the graph cuts the vertical axis at 0. In fact this line is the...

  • Hi Pete - yes you are right. Strictly we should say "the larger the modulus (or magnitude) of m, the steeper is the line. This would then cover both positive and negative cases. Thanks for pointing this out.

  • Dear Angela,
    thanks for the comments. I am pleased to read that you have found aspects of the course helpful. Alas, it is not possible to access the course without going through FL, but your colleagues and students can still register today and that will continue to give them access.
    Best wishes,

  • Dave, thanks for your helpful and insightful comments. Just for future reference, there is an enormous amount of supplementary material freely available on and also on (in the latter course the material is organised more like a full course - arithmetic, algebra, ....). I am sure the FL team will find constructive the...

  • Hi Philip. In the week 3 course there will be plenty of example of how straight line equations occur in the decription and analysis of scientific and engineering problems: distance, time, speed, acceleration, force, reaction rate ...... I hope this will help solidify your understanding and enable you to see how these techniques are relevant to the work of a...

  • Thanks for all the week 1 comments. In week 2 we develop the vocabulary introduced in week 1 and start to see mathematical definitions of points and lines. Graphs of straight lines are vital tools not only in the physical sciences and engineering but also in the bio- and social sciences.

    In respect of the social sciences in particular, the Nuffield...

  • The sequence of horizontal lines in g can be thought of as a pattern which repeats itself regularly - we call this sort of behaviour 'periodic' and lots of important graphs are periodic. It also looks a bit like a wave made up of square pieces - engineers call these 'square waves'.

  • hi Martina, can you be a little more precise about which bits you don't understand, and I will see if I can help.

  • I will do my utmost to dispel that horrible cringing feeling, and hope you feel much better about maths by the end of the course! I don't think there is anything to be afraid of in the next three weeks.

  • Hello all, and thank you for your candid comments. It is gratifying to see that there is already a wide range of learners from around the globe signed up. I hope you all get something valuable from the experience!

  • Roberto - many thanks for this. I hope your new-found knowledge does indeed help with the home schooling.

  • Ian - thank you for your contribution. I can assure you that there are many students in UK universities today that need this level of help. My colleagues and I support them everyday. Of course, there are many others who are already doing much more advanced mathematics, but because access to higher education has widened so much, a great deal of work is going on...

  • Hi Reino - the primary audience for the course is those students who want to study a foundation course in science or engineering. In the UK such courses (often called Access Courses, or Year Zero courses) help those students have not got particularly strong maths backgrounds in the Year prior to starting an engineering or science degree.

  • You could try and choose a more suitable size.
    May be I should download some variations and include links to those too.

  • Don't worry about learning slowly - remember some of the world's best mathematicians took a lifetime to achieve their understanding of some of the fundamental ideas. We all progress at different rates - what is important is that you are not deterred. Take your time - and ask for help.

  • Many thanks for this additional emphasis. Tony.

  • Hi Colin - we discuss this particular issue in the Quiz in section 3.16 (Q10). I avoided introducing it at this early stage because I wanted to concentrate on the equation of the line in the form y=mx+c. There is an alternative form (ax+by=c) which embraces vertical lines too but then to extract information about the gradient and intercept we need some...

  • Thanks for the comment. Week 1 was intentionally different from what learners might have experienced at school level. It will get more challenging in the next couple of weeks, but I am trying to strike a balance between overcoming some learners' lack of confidence and the need to consolidate material which will be important for those who want to go further in...

  • Some great images - keep them coming. As a musician myself, I particularly liked the guitar!

    Also, some really nice photographs of lines and curves in the man-made and in the natural world. If we can get learners to see that these mathematical concepts are around us all the time, perhaps we can break down some barriers to learning.

    Thank you

  • Hello everyone; welcome to the course. Thank you very much for your all your introductory comments and for being so open and honest. It is great to see such a wide range of learners, different motivations, and from many different parts of the world. I shall look forward to hearing how you are getting on as the course develops over the next few days and weeks.

  • Dear Ann,

    Thank you very much indeed! Much appreciated by the team!


  • Thanks Chris - this is something I believe very strongly. It is a matter of steady, careful and patient progress. Many more people could understand more and develop their mathematical skills in the right learning environment.

  • Thanks for all your comments Barrington. In the majority of case, the helpful and encouraging comments from others taking the course seem to have sorted out people's queries.

  • Tony Croft made a comment

    Thank you for all the interesting discussion about Q7 in 2.26.

    In the equation y=mx+c, either or both of m and c could be zero.

    If just m=0, the equation becomes y=c and whatever the value of c, this is a horizontal straight line with vertical intercept (0,c).

    If just c=0, the equation becomes y=mx which, as we have seen, is a straight line through...

  • Thank you Lourdes, and I am delighted that your love of maths has been reignited.

    I take your point about mathematical applications in business, but the target audience for this specific course was those students who aspired to start Science and Engineering Courses and was intended to ease their transition into the mathematics they would need early on...

  • You are absolutely right Tony that an infinite number of straight lines can be drawn through two distinct points if we are prepared to draw lines of different lengths. Mathematically though, all of these lines will have the same equation. It is in this sense that there is a single line.

  • Thanks for so many amazing images of lines and curves in the world around us. Great to see such enthusiasm at the start of this course.

  • Hang on in there Karen - don't over worry about the metre per second. This won't be a critical part of what is to come.

  • Nadia

    don't worry about the negative powers for now. They do not form a crucial part of the work in this course. We have included a link to a resource on negative and fractional powers - this is for further reading and for completeness only. Best wishes with what follows.

  • Hi Paul - the course should be well-suited to people like you. I hope we can convince you that you have the potential to be good at maths!

  • Thank you to all on this thread. I have tried to respond at length in my end of week email to the issues about: the level of the course, who it is aimed at, calculus as a prerequisite for science and engineering courses etc. A significant point is that thousands of students entering university to read science and engineering have done NO MATHS beyond GCSE....

  • Eddy - you will find plenty of applications and practical examples in Week 3 including from mechanical engineering.

  • Please could you resend the specfic query. Thanks.

  • Thank you for all your various comments. As in the previous incarnations of this course we have a very broad mix of learners - many very familiar with the material who find it rather easy, and many others who find it challenging. Please bear in mind that our primary audience comprises those learners who need to build confidence from a shaky foundation and who...

  • Phil, Ged
    thank you for these helpful observations. I am going to look into this to see if we can improve the wording. A big challenge in a course like this is to provide an accessible, and very simple definition in just a couple of sentences, especially when most of the learners will not have met terminology such as EMF, impedance. etc. As I said, we will...

  • Dear Michel,
    I am not really sure what you are saying here. If the starting point was (-3,-4) and the end point was (2,6) then the equation of the line would NOT be y=2x. Neither of your two points satisfy the equation y=2x. In fact, the line that passes through your two points has equation y=2x+2. The line y=2x passes through the origin - yes (0,0). Later...