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
Activity
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Tony Croft made a comment
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')
datafailed, 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...
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Tony Croft replied to Tony Croft
thank you very much John.
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Tony Croft made a comment
Hi. Just completed the exercise using Jupyter notebooks on SageMathCloud (cocalc.com).
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. -
Tony Croft made a comment
great intro - many thanks, loved the bird and the 'right-way around' map.
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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.
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Tony Croft replied to allan beer
Many thanks Allan.
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Tony Croft replied to Gladys Moreno S.
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... -
Tony Croft replied to Pete Coulson
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.
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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,
Tony -
Tony Croft replied to Dave Ingles
Dave, thanks for your helpful and insightful comments. Just for future reference, there is an enormous amount of supplementary material freely available on www.mathcentre.ac.uk and also on www.mathtutor.ac.uk (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...
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Tony Croft replied to Philip Frampton
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...
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Tony Croft made a comment
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...
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Tony Croft replied to Judah Attille
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'.
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hi Martina, can you be a little more precise about which bits you don't understand, and I will see if I can help.
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Tony Croft replied to Judah Attille
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.
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Tony Croft made a comment
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!
Tony -
Roberto - many thanks for this. I hope your new-found knowledge does indeed help with the home schooling.
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Tony Croft replied to Ian Bruce
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...
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Tony Croft replied to Reino Warren
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.
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Tony Croft replied to Leigh Hughes
You could try http://www.printfreegraphpaper.com 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.
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Many thanks for this additional emphasis. Tony.
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Tony Croft replied to Colin Webb
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...
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Tony Croft replied to Bev Courtney
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...
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Tony Croft made a comment
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
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Tony Croft made a comment
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.
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Dear Ann,
Thank you very much indeed! Much appreciated by the team!
Tony
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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.
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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.
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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...
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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...
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Tony Croft replied to Tony Samson
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.
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Tony Croft made a comment
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.
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Tony Croft replied to karen rann
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.
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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.
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Tony Croft replied to Paul Scowen
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!
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Tony Croft replied to James Buckley
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....
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Tony Croft replied to eddy mayne
Eddy - you will find plenty of applications and practical examples in Week 3 including from mechanical engineering.
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Tony Croft replied to S Jones
Please could you resend the specfic query. Thanks.
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Tony Croft made a comment
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...
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Tony Croft replied to Phil Thress
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... -
Thank you Cathy-Anne! Then it has all been worthwhile!
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Jennifer.
The use of "minus"and "negative" is a little confusing I think. Often these words are used interchangeably, so a negative number like -8 might be referred to as "minus eight" or "negative eight". You are correct: the minus sign is also used as an operation for combining two numbers as in 8-2, read as "eight minus two". We would not say "eight... -
Islam - You are quite correct that a graph is a pictorial representation of a relationship between two variables.
But there is some misunderstanding here about the distinction between a single point, as in (7,0), and a collection of points from which a graph can be constructed.
If the horizontal axis represents time, then the point (7,0) tells us that...
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Tony Croft replied to M L
Hello Max
I don't think you should worry about "memorising the Greek alphabet". If and when you need to use any characters from this alphabet then familiarity will come naturally. Most of the letters are not commonly used anyway.
Good luck with the rest of the course.
Tony
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Tony Croft replied to James Bowater
Hello James. You are absolutely correct, and despite all our careful checking this has slipped through. We have now amended the question. Thanks once again for your attention to detail!
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Delighted that you have been able to get a group of employees together and that the experience has been so good for you/them. I would be very interested to learn more about things like whether they saw this as a joint enterprise, whether they helped each other etc. It might provide a good model for more work-based training (a.c.croft@lboro.ac.uk)
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Tony Croft made a comment
Many comments along the lines "I must progress at a slow, steady pace". In the pre-course blog I wrote “to be good at maths” should not mean “to be good at doing it quickly”. The world’s greatest mathematicians spend their lives trying to tackle problems! Having time to think, self-pace, revisit the materials give students a dimension to learning that was...
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Now that this course is coming to an end, we will be reviewing what we have learned and looking at where we go next. Differential calculus is a likely topic. Watch this space!
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Tony Croft made a comment
A lot of discussion re Q8 on Quiz 2.26. Quite right too! Well done to those who have spotted there were two false statements - not one as suggested. We are looking into correcting this. The third option - "It is impossible for both m and c to be zero at the same time" - should have read: "It is POSSIBLE for both m and c to be zero at the same time" - which is...
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The course has been designed for those who are aspiring to study *foundation* courses in science or engineering, and particularly those who lack confidence in mathematics. Many students joining such courses have not done any mathematics since GCSE, and then often several (or many) years before - please see my earlier post regarding information from the Royal...
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Tony Croft made a comment
I am delighted by the positive responses of so many learners. Over the years I have tried to support students who have not yet grasped the fundamentals and consequently fail to progress. Many science and engineering foundation students that I, and colleagues around the UK, support on a daily basis lack confidence with the sort of material presented here - ...
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thanks John. As you will realise, this is out of my control, but I will certainly pass this on to FL.
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Tony Croft replied to Kathleen L
Hello Kathleen,
there is no real need to memorise the Greek alphabet. You need to be aware that symbols from the alphabet are used, and know where to look them up if necessary. The main point is not to be intimidated by symbols you are perhaps not used to. -
Hi Isabel.
I am pleased you are enjoying the course so far! Of course you are right - whatever *you* think is the most sensible within the context in which you are working is indeed correct. At the same time you need to think about how you would communicate your ideas to others in ways that they are most likely to understand. Furthermore, it makes some sense... -
Tony Croft replied to Mary Ormsby
Mary, thank you very much for your feedback.
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Thanks - I would emphasise again (as I wrote in some detail at the end of the week 3 discussion) - that the course aims primarily to support those wanting to start a foundation course not the first year of an undergraduate degree. I agree that further study is essential and in the final sections of Week 3 we indicate those areas which need to be tackled next.
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Very helpful David - thank you.
Thanks also for your other very helpful contributions this week. -
Tony Croft replied to malcolm davis
Thank you Malcolm. Development of this first FutureLearn on-line maths course has been a learning curve for all involved. The experience gained will help shape development of more advanced mathematics courses in the future.
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Tony Croft made a comment
I appreciate that some learners have found the material too easy but this is certainly not the case for all, and the course set out to better prepare those who aspire to study science or engineering foundation courses at university and who need to develop their mathematical confidence. Note particularly the use of the word "foundation", and not the "first...
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Benjamin,
thank you for this comment. The idea of extension material is definitely something we will be looking into for a future run. At this first run our priority was those leaners who definitely don't feel confident. Tony.
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Hi Claire/Paul - there is certainly no need to remember this alphabet at all. Know where to look it up when necessary. If you are ever in a situation where you need to use these symbols, gradually you will become accustomed to them.
