Teaching a Statistics course

This semester, I will be venturing into teaching statistics course along with my colleague Prof Kavita Isvaran. This is going to be quite exciting because I have only taught mathematical ecology (and its variants, basic to intermediate to advanced) so far.

Of course, Kavita has been teaching this course on Quantitative ecology, with a focus on both research design and statistical inference, for almost a decade. This course has undoubtedly transformed the quantitative skills of our students and they way they design and analyse their PhD thesis projects.

This year, the main change to the course is as follows: we will cover less material but will add depth (the breadth will be added in a second course in Jan 2019). While Kavita will teach Research design in the first half of the course, I will teach basic statistics – starting from probability distributions to point estimations and linear regression – in the second half of the course. We really want to ensure people understand basics of what they are doing – including associated math and programming.

We will be assisted by our joint PhD student Aakanksha to conduct tutorials in math, R, grading assignments, etc.

Media coverage of our winter school modern finance and macroeconomics

Along with my collaborators Srikanth Iyer and Srinivas Raghavendra, I am organising an ICTS conference on “Modern finance and macroeconimics” from Dec 22nd and Jan 2nd.

We are delighted that our school got a coverage from Deccan Herald, an important newspaper in southern India. My colleague Srinivas Raghavendra and a student participating in the conference are quoted in the article.

In this school, I will be teaching techniques related to our collaborative work on testing predictions of early warning signals of critical transitions in financial markets. This work was done with Srinivas Raghavendra and my former UG students Nikunj Goel and Quentin Hoarau.

And Happy new year to all!

Summer updates by Vishu Guttal: Teaching, travel, and talks

Its time for updates again!  Let me start with myself and will post separately on what students have been upto.

Teaching: In the Jan-April term, I taught the course EC 201, the introductory course on Theoretical and Mathematical Ecology. This was the fourth time that I was teaching this course, but one thing had been bothering me a lot: the course was becoming increasingly inaccessible to biology students (in particular, our own CES phd students). The reason was that once UG students of IISc who had much better math background began to take my course as an elective, the mathematical level of the course became too difficult for CES PhD students many of who come from Masters in Zoology/Botany/Wildlife biology programs where the emphasis on math is minimal to zero. I did not want to miss out either on the UG students so that they are exposed to cool ideas of mathematical ecology or the CES phd students who ought know basics of theoretical ecology. Based on various suggestions, I tried this new solution: which is to let UG students take my course only on alternate years.

So this year, I restricted the class to biology majors who have had little exposure to mathematics. The UG students of IISc were requested not to take the course this year (and they kindly obliged). I thought that this really helped the biology background students to learn at their pace — and they did really well. So I am going to keep this format for the future. Even years: the course is open for all. Odd years, the course is open only for non-math background students.

Travel:  In the second week of June, I went to visit my collaborator Dr Sonia Kefi at Montpellier, France to initiate collaboration on our Indo-French grant from IFCAM. We started off great on a project on spatial pattern formation that will be led by a member of Sonia’s group. Sonia and her team members will visit Bangalore in December and we hope to keep this on for several years!

Popular talk: I gave a couple of popular talks/workshops this summer. One was at Christ University, as a part of the initiative by National Network for Mathematical and Computational Biology (NNMCB) to reach out to local colleges and universities. I spoke about evolution and collective movement in animal groups.

Workshop: I then gave a set of lectures at NCBS at the Monsoon School on the Physics of Life. The audience here were basically a bunch of highly motivated kids from various parts of the country studying physics, math or engineering. The idea was to expose them to biology through the lens of mathematics. I started off showing a graph from Ives et al 2008 paper on how midge populations change over time, and how can we construct a mathematical theory of the same. At the end of four hours, students learnt all the way from building simple model of exponential growth to logistic models to constructing bifurcation diagrams for a consumer-resource model. They were all super delighted when they found that even small changes in external factors can lead to large changes in populations; mathematically, this is captured by saddle node bifurcations.

An ecology course at IISc from Aug-Nov 2013 for anyone interested

I will be offerring a course at IISc on the basics of ecology though the lens of mathematics. The details are as follows. Feel free to spread the word to those interested:
Course title: Ecology through numbers
Instructor: Dr. Vishwesha Guttal, Assistant Professor, Centre for Ecological Sciences, IISc (Website: https://teelabiisc.wordpress.com/).
Class hours: Monday 6pm – 8pm. Wednesday: Computer lab hours to be decided.
Start-end dates: Aug 2013 to Nov 2013 (approximate).
About the course: Ecology is often understood to involve only field work. The aim of this course is to show how simple mathematics has played a central role in ecology. Syllabus includes how to develop simple mathematical Models in ecology; Models of population dynamics; Chaotic dynamics; Predator-prey cycles; Tragedy of the commons, etc.
Intended audience: Anyone outside the regular IISc academics with keen interest to learn ecology. CCE is a centre at IISc has been offerring regular semester long courses over years in the evening hours so that working professionals, scientists, conservation enthusiasts, engineers, amateur naturalists – pretty much anyone with a bachelor’s degree – is able to attend the course.
For more details on the CCE and its objectives, visit this webpage:

Eligibility: BE/B Tech./M.Tech in any disciplines, Or masters (M.Sc., MA, M.com) in any discipline.
Pre-requisites: Math at the level of High School (Basic calculus) and some Programming experience would be helpful, but not, MUST.
Course-fee: Rs 7000 for the entire semester. Please see the website for details of application procedure and how to make the payment (dont forget to check terms and conditions regarding fee payment):
Any questions regarding course content, etc can be sent to me at vishwesha.guttal@gmail.com
For queries regarding procedure to enrol, etc, please contact the CCE office admin directly.

Summary of course evaluation on Theoretical ecology course (EC 201) in Jan – April 2013 semester (Updated)

Like last year, I took students’ opinion/evaluation of my course. Unlike last year, this year the course was taught for the complete semester, allowing us to cover more topics and do better on projects. Before I go onto summarizing the course evaluation, here was the composition of the class:

* Undergraduate students: 10 (Nine of them from IISc and in their 4th semester; they were taking electives for the first time. Of the 9, six were from Math major, 2 from Biology major and 1 from Physics major. One UG student was an international visitor – from France – with computer science major).

* PG Students: 7 (4 CES PhD Students; 2 NCBS PhD Students and 1 M.E student from Chemical engineering).

* [UPDATE]: Auditing Students: I entirely forgot to add that there were roughly 6-10 students who audited the course; most of them fron non-math background. They were equally active in the class, in doing (most of) class assignments, etc.

Clearly, having 10 UG students was a major surprise but the overall mixture added lot of value to the class by allowing a diversity of perspectives and skills. Writing more about this requires a separate post! So, let me move onto the summary of course evaluation by students.

1) How do students self-evaluate their understanding of various components of the course? Course_understanding_EC201_2013Clearly, on an average the distribution peaks at “Good” and “Very Good”, which is great! Compared to last year, the distribution has moved towards “Very good”. More specifically, topics that were mostly rated as “Good” (Discrete population dynamics, continuous population dynamics and stability analysis) have now moved towards “Very good”.

However, the topics where I need to improve (so that students self-evaluate with higher scores!) are the topics I added this year, so I was teaching them for the first time. The reasons seem quite obvious! These are evolutionary dynamics and two-species interactions.

2) How good was the coverage of topics? Course_coverage_EC201_2013A very nice distribution that peaks at around “Adequate”. But with a clear right-skewed distribution, suggesting that most students wanted me to cover more of pretty much most of the topics – which is not possible given the time constraints. Here is what one of the students commented about this question:

the options given r not good, like a little more detail is always Helpful!! Adequate with respect to what?? w.r.t exams or w.r.t interest in the topic?? 😛 ( dnt mind!! 🙂 )

I thought that was a very good point, and that is clearly reflected in the average response of students. The response is exactly same as the previous years where the average response was that more details are needed on many topics! The best I could take away from the above plot is that more on two-species interactions and evolutionary dynamics would be appreciated. Anyway, the same student also said:

Coverage and depth both wer (sic) nice, as most of the times it went according to the students! It was good!

How should I rephrase the question next time, or should I entirely skip this altogether?

3) In general, the ratings on lecture notes and quality of teaching were pretty good (both above 4.25 on a scale of 5). Compared to last year, both have improved. In particular, I had hardly given any lecture notes last year. This year, we recorded all classes and they were available on the course website – typically within a week of the class. Lecture notes were prepared based on transcribing the videos and also posted on the website. I had employed two TA’s specifically for these purposes and they did a splendid job, I think. Although I don’t know if anyone really used these resources, we had made our effort.

Work load was rated at 3.58 – but I dont know what that means. Again poor phrasing of question (the options ranged from “Very poor” to “Very good”). I can make sense of “Very good” but what does average workload mean? Did students want more workload, or less workload? Last year, they explicitly said less workload would be better. Although it’s hard to imagine students asking for more work load, I think I can expect something counterintuitive from this class ;-).

4) What other topics would you have liked to learn?

Most commenters perhaps realized that it is difficult to cover more topics in the semester. But two suggestions that one student had was to include meta-population dynamics and island biogeography models. Great suggestions, even if I can not cover them in a class, I should consider doing a workshop at ces.

A very useful suggestion is to talk about interesting history behind mathematical models and concepts. I will try this next year, after learning myself more about them.

5) General comments to improve the class further: 

A common point that came in 4 of five comments was that

Mathematics is clearly very important for this course.

and since ecology students come with not much math background (some may have taken their last math course in their 10th class),

some fundamental Mathematics [and programming] classes would be useful for non-math students.

We did have TAs teach basic pre-requisite math in the course. But I suspect a full fledged course on math and programming prior to this course would make a difference to many ecology students. Unfortunately, there is no bandwidth in the CES, as of now, to add a new course.

Class room programming sessions cannot be called a success as not all students were well versed with the R language. …  Atleast 2 classes of basic R is mandatory to be freely usable even during exams.

I don’t know how to resolve the above problem on programming language. I thought that TAs did do tutorials on R – at least in some rudimentary way and were usually available during programming sessions to help students. And many students as far as I can tell did well in those sessions. No doubt it needs to be better done.  I Another related point was that

But probably due to a skewed structure of the class where majority of students have a strong mathematical background, the purpose of the course for ecology students ( who usually don’t have a strong mathematics foundation) tends to get lost.

I really hope that was not the case! If this course were really to be taught only to those with strong math skills, it would take a very different trajectory (and not necessarily a good one). I think having this extreme set of students added a great value to the course.

One possibility that some faculty at CES have been thinking is to make an online basic math and an R programming course (such as those from udacity or corsera taken in the Aug-Dec semester) a pre-requisite for my course (in Jan-April sem). Going through online classes can get boring, so we should assign some TAs and mentors so that there will also be some discussion sessions to clarify doubts and to ensure there is no attrition.  One thing that we have decided in our department now is that my colleague Kavita Isvaran’s course on Quantitative Ecology 1 will be offerred in the Aug semester from 2014. This course covers some stats and programming could also help students when they take my course. 

maths and ecology students should be assessed separately.

I have thought a bit about this since the beginning of the course but am unable to justify separate grading schemes. One way to think about this was that if a math student were to go and take a hard core biology course, would he/she be graded differently? Most likely not. Even within this course, standards of ecology were maintained same for both math and non-math students. Anyway, something worth thinking again but for the next year. Despite all these issues, I found non-math students who had very little math and programming experience did exceptionally well in the course.

Here is one other critical and very useful comment:

 Projects, I feel were not graded very satisfactorily. At the least the student should know the categories upon which the project was graded upon so that in the bare minimum, even if he/she gets a not so good grade he/she will at the least know how to do/present a project in futureby correcting appropriately.

Good point  about project grading. I am usually very careful in mentioning something like how grading is done, but as the course progressed, it slipped out of my mind to remind students about how things are graded in ase of projects. But point taken.

Its always good to end with a positive light-hearted comment:

Prof, TA’s, AC in the room, and cookies in the break..everything is Very nice!! 🙂 really liked and enjoyed the course!! 🙂 and I really appreciate the way the class was handled by prof, I mean extreme Bio n extreme maths people at same time!!! :O 😀

Thanks to all students for being part of the course! Special thanks to TAs Sabiha, Jaideep, Sumithra and Nitin for fantastic help that you all offerred throughout the course.

Summary of feedback on Jan 2012 module on Theoretical Ecology

I should have written this really long ago, but finally I get to do this.

Although teaching evaluations where students get to grade teachers are a norm at most places in the world and also in India (like IITs), here at IISc there is no formal evaluation of our teaching. So many of us informally collect anonymous feedback from students. For the half-a-semester module on Theoretical Ecology that I taught in Jan 2012 semester, one of the students (Karpagam Chelliah) helped me set up a survey online and got responses to questions I had set up. With my full semester course on Theoretical and Mathematical Ecology set to start next week, I thought this is a good time to see those feedback again. Here is what I found:

1) First of all, should the half-semester module on theoretical ecology be converted to a full semester course?

Overwhelming feeling among many of my colleagues was that, yes, it should be. I was not so sure, until I saw results of the survey.

All the students who took the survey (total 13) said we should have a full semester course!

2) Now to some details, as to how students self-rate their understanding and how well were the topics covered.

I was able to cover two basic topics, (a) single species population dynamics and (b) random walks and its application to animal movement. In this survey I  subdivided these two broad topics to overall 6 components: (i) Discrete population models (ii) Continuous population models (iii) Stability analysis (iv) Random walks and animal movement (v) Programming and (vi) Overall course.  Student had to rate their understanding for each of the above components, and how well/detailed each of the topics were covered.

This first chart below shows how students self-evaluated their understanding of various components of the course. Y-axis represents percentage of students who gave that rating.

Here, bars on the left side means I should be concerned, and work harder to improve those aspects. Two components that I did no teach well are stability analysis and programming, the math and the computing parts of the course!

This next chart on the right (where a central peak is the ideal response I would like to see) supports the same view with quite a few students suggesting that I covered less than adequate on both stability analysis and programming.

As a corrective measure, I plan to have one week exclusively dedicated to programming. I should also have more discussion, worked examples and assignment questions on stability analysis which is an extremely fundamental and useful tool for ecologists.

3) I had asked for general critical comments on the course. As you can imagine they are very helpful and here is a summary:

What was good:

It seems students liked discussions we used to have in the class. One student said  “The course encapsulated modelling really well and helped banish some fears of the same.” That was precisely the goal of this course, so it was glad to see that the course achieved that goal to some extent (although its only one data point!).

Some particularly liked how I used to recap ideas from previous classes before going onto what next (I learnt this from some of my teachers because those were the only classes I could understand well). Some thought there was enough scope for thinking independently in the course and that assignments were “thought provoking“. But as you see below, there is lot to improve as well.

What needs improvement:

Assignments and Workload: Four students (that’s 25% of the class) commented that workload was too much for half-a-sem course. On the other hand, one student thought many calculations done in class could be moved to assignments so that we can discuss more in the class.  One student said “please give adequate reading material. Even though I understood what was being done in class, I forgot everything upon coming back home”!

Clearly, balancing these contrasting needs of reducing workload while increasing reading/assignments is not going to be easy! One student had a suggestion that short and frequent assignments could be more useful – I think this may satisfy both sort of students and this is what I am planning in the coming semester.

Other suggestions were to include empirical data with models, how to validate models and how models can be helpful with conservation. This is not easy given time constraints, but I can try with one or two examples from my own research work. One student said course should be better structured, and I entirely agree with that because I know how haphazard my preparation was especially with respect to assignment and reading materials.

One other important point was that some math and programming background can enormously help this course. Our biological sciences division does offer a basic course on Math and Stat but it is offered in the same semester as this course. It would be ideal if students come prepared with math and programming in Aug semester for two quantitative ecology courses in Jan (the other one being highly sought course taught by my colleague Kavita Isvaran on Quantitative Ecology: Research Design and Statistical Inference).

4) What other topics should be covered if its a full semester course?

Almost all respondents said “Evolution” (more specifically, evolutionary dynamics, ESS and Game theory, population genetics, etc). There were also suggestions on predator-prey dynamics, host-pathogen dynamics, more on chaos and animal movement, etc. Clearly, evolution is the winner and I plan to teach this for 4-5 weeks. I also plan to teach structured models and spatially explicit models in ecology. This may come at the cost of studying more classic models like competition and predation, but I feel that with the kind of background that this course offers, students should be able to pick up a text book and read it on their own.

What do you think? What topics should a basic theoretical ecology course cover given that students basically come with no math/programming background?

Jan-April 2013: Course on Theoretical and Mathematical Ecology

I will be teaching a course on Theoretical and Mathematical Ecology (EC 201) in the coming semester, Jan-April 2013. I am very excited about this because this is the first time I will be teaching a full-semester course. I did teach half-a-sem course in Jan 2012 semester on Quantitative Ecology where I taught a module on theoretical ecology (my colleague Kavita Isvaran covered Statistics). That experience was invaluable and got very useful feedback from students on how they liked the course, and what can be improved.

Watch this space for more updates.  Tentatively, we will have our first class on one of the days on Jan 2-4.

Quantitative ecology: mathematical modeling in ecology (module two)

I will be co-teaching Quantitative Ecology with my colleague Kavita Isvaran in the current semester (Jan-April 2012) at IISc. This is the first time I will be teaching a course will involve extensive lectures (I have taught recitation/tutorials/workshops before).

There are two modules to this course. The first one is on Statistical methods in ecology: this is taught by Kavita for the first half of the course. I will be teaching the second module that is on Theoretical ecology. Tentative start date is Feb 27th 2012.

Watch out this space for more!

Our workshop at YETI covered in The Hindu

The workshop ‘Ecology through numbers’ at YETI (also see this), the student ecology conference held at IIT Guwahati last week, was nicely covered in The Hindu.

Young Ecologists Talk and Interact (YETI) 2011, now under way at the Indian Institute of Techonlogy-Guwahati, witnessed a unique activity on the second day.

Instead of interaction on ecology or conservation, participants in one of the workshops were asked to do an arithmetic exercise using calculators. They were amazed at the results they got as they had no idea that these could be related to studies in ecological sciences.

It was Vishwesha Guttal, assistant professor at the Centre for Ecological Sciences (CES), Indian Institute of Sciences (IISc), Bangalore, who demystified mathematical modelling of ecology for the young ecologists.

The conference was great in many aspects, and I hope to write a bit more in detail on that soon!

Workshop on simple mathematical models of ecology

I will be conducting a short workshop at YETI (Young Ecologists Talk and Interact), a conference organized by, and for, students of ecology in India.  This conference started fairly recently, in 2008, and has become very popular and successful. I was delighted when I was invited to conduct a workshop on mathematical ecology, and readily accepted. An added attraction of this year’s workshop is that its going to be held in Guwahati, the gateway to the north-east of India!

The workshop is titled “Ecology through numbers”, and its blurb reads:

The aim of this short workshop is to show that simple mathematical models of ecology are not all that mathematical, and they can be learnt by anyone with basic skills in arithmetic and algebra. So, no prerequisite, other than a keen interest in playing with numbers, and making biological sense of it, is needed. The workshop will involve doing some hands on numerical ‘experiments’! So, please bring a scientific calculator that you are comfortable using, and a few blank papers.

The conference also has other workshops (including one on statistical methods) and interesting plenary talks. Looks very exciting! This article in Telegraph covers the upcoming meet, and also mentions about our workshop on simple mathematical models!