Good evening, everyone, and thank you very much for choosing to spend your time with me, for being my companions tonight. I think I was one of the first, members of staff who gave a lecture, actually, in, computational mathematics, when the room was refurbished And that I can tell you today I have a much better turnout than I used to have for my lectures This being, mathematical lecture, I wanted to include some quizzes as well, but I decided to, to skip them.
Yes And let's, let's start the journey So this is the outline of the talk So I'll start with a brief journey And then what is mathematics? I think we all have some idea or some perception of what the mathematics is, but we'll see what other people say about mathematics then some maths metaphor.
To me, mathematics is the language of God, because I think it's one of the greatest gifts we have. And with mathematics we can see some things which cannot be expressed by poetry and even by theology. So mathematics is not able to only state things, but is able to prove them as well So this is why we are going to discuss about some of my favorite maths metaphors, which include infinity and then fractals.
Then I will show you some maths research, which is pure and applied, and then some, some, details about maths support for all. In my description of the talk, I mentioned, like innovation in pedagogy and so on, I would like to, to mention that I am not like an innovator who pursued innovation for the sake of being an innovator, of trying to do something new But, I was, in the classroom, I was running, I was thrown in front of the students, I had 150 students in my first lecture, and I had to find a way to interact with them. Most of the students did not want to be there and hated mathematics.
I was teaching computation mathematics to the students who hated mathematics. I had many students who are mature students, I had many students who were, with various learning disabilities, and you had to find a way to teach them all and that actually, this led to all these innovations. So, it was just driven by the need to, help the students And, during my time as a lecturer, I learned this golden rule of teaching maths.
So master the truth Nothing but the truth, but not the whole truth. So that's why I will skip many of the, proofs. Also, I'm very delighted to see that I have some former students in the room They do not know that they appear on the slides.
So this is a quick profile summary I did, PhD in applied mathematics in University of Nottingham Then I completed a PhD in pure mathematics. I will tell you a little bit about how that happened I been Erasmus and Turing scheme coordinator, so I really wanted I will tell you more about what I found when I arrived in Derby.
And then I was very keen on developing international collaborations I think this is something that university was really lacking And then even when we were having some collaborations internationally, the students, our own students did not know about those and the benefit of the opportunity And then in the recent times, I became program lead and program leader and the leader of these partnerships in China I showed that map.
So this is like a pretty up to date map of, the places, I visited I would like to mention that I never visited the place without giving at least one talk, sometimes seven talks, And I think one reason why people invited me, kept inviting me, was that I tried to never say no. But this meant that I had some amazing opportunities And, now, before we really launch ourselves into the journey, I have an invitation for you.
So if you see any small item that could help your students, please take that Then implement it And that will make me very happy I've been involved with the University of Derby, so I think my journey is also the University of Derby, from a place which was mostly teaching focused, local, along this amazing journey as well, because during my time here we expanded significantly Erasmus opportunities for the for teachers and students Then we joined the world university rankings in the top 20 universities.
So when I joined Derby, Derby was not even in the top hundred universities in the UK For me it was amazing When I think through some things that where I contribute, I played a little part as well The university joined the top thousand and then the top 800 and then we've been like 500 to 600 So I think we are really going up and up then tenfold.
Teaching excellence framework again, the university provided excellent teaching experience to the students throughout, but then to get this rating as well, nationally, only 27 in the previous step, I know that 27 universities out of 150 I don't know exactly how many, but I know that only 27 had gold So I was very happy to be part of this journey And now the Turing scheme So my, journey started in the next.
Have you ever heard of that? Next You know, this is a small town in the middle of nowhere and of train line, near the mountains, five kilometers away from Dracula's castle Maybe this put it put it a little bit on the map Now we have an airport nearby as well And, I had a happy childhood.
I was mostly in the trees. My, my, cousins were making poems about us just being in the in the tree Then, when I was, dressed in, in, orange, we were reciting some communist poems So that was still communist Romania And then this is my first school day with my lovely mum, who provided and really lived for us.
I met infinity through my mum I, we were playing a numbers game in the, in the, in the nursery and we were playing who could say the, the biggest number and we were saying ten 100, 1000, 1 million, 1 billion, 1 trillion And then I went to my mum and asked her, what's the biggest number? And my mum said, an infinity of infinity that does not exist as a number It's not the number But I was winning all these arguments and that was the first time I was that made me think.
Then I went to primary school My first grade was 90%. I was very proud, right? I was telling my mates, look, I've got 90% I'm, my mum was not impressed I got some feedback from her and then I learned not to mess up with mum.
And, I knew that, mum expects me 100% because she was giving her 100% So I was very privileged from this I had an experience in the classroom with, this is my primary school teacher, Aurelio Russo And, he stretched me during the class My mom was asking me to do maths, but I did not really like it.
And, this teacher asked me to go to the front of the class and write the proof on the board All my mates failed, and I thought I would be safe as well But he said, no, no, if you don't prove I fail you and then something activated and I was able to write the proof completely I said no So actually I can do it.
And then, I started in the secondary school We have a very intensive maths competition program in Romania It's quite heavy The students are thrilled You have local competition, county competition, national level competition.
But I was in the middle of nowhere I did not have like special training like you have like in the in the camps for maths Olympiads, so on I was still from the small school in that next. And then I met this lovely teacher Luciano Dato and with my teacher we started to practice a little bit for these competitions Then when I was in in year six, I came fifth in the county competition.
And then I promised my teacher next year will go to national level, And she said yes, yes, never You know, no one from our school ever went that far So don't worry. And then next year I had the perfect score in the in the competition at county level, and I had to qualify to national level.
But because I was from the countryside, I was put aside They deducted two points for nothing This teacher went to appeal to county level with the director of the school, and we were allowed to have a competition only between the guys from the countryside And then, yes And and I, I was fortunate because I got ill that period for a month and I could practice properly, and I solved all the books I could find, and I came on top.
And then I went to the National level, and I was the best student in the whole county for all levels I had the price But then next year I wanted to have the top prize in the country, and I was praying I did not go to the church at that time I did not know much about church and my prayer was, I want God, I want wisdom, I want to be first in the country in maths That was my prayer, a simple prayer.
And then through snow, through snow, through rain and snow On a Sunday I was going to my teacher every Sunday and I was solving problems six hours, eight hours a day after class And then some days I was going to my teacher to discuss Actually, it was like the brainstorming in two and the it's I'll cut all the stories short But what happened was that, against all adversity, I went to the national competition.
I could not sleep for two nights because of trains, because of stress and so on But when I went to with the to the train the night before, I had the meeting with the teacher, and I gave her two problems that I could not solve In the morning this teacher came, did not sleep, and came with the solutions in my mind I figured them out because I was very focused and during the sleep I could solve that But my teacher, you know the image of this teacher stays with me.
And this teacher is in this room today, So it's like the support. Yes Then, I went to high school in the best, high school in the country, in the county And, And now I wanted to be the first in the world.
And I am very happy I did not, I lost focus, I started to spread out, like Stephane mentioned So I still, now I realised that I could do choir, I could do I was in the rugby team, I was in the, basketball team and so on So I think I was doing too many things But then salvation came from somewhere else Salvation came from.
So I had a teacher in the class, and this teacher showed us how you can do mathematics with humour. So we when when your students are stressed, if you tell, like, the right joke at the right time, you can you can reduce the tension in the classroom And then I was very fortunate because aged 15, I met a teacher who was, of Hungarian origin This guy met Erdos So he’s a famous mathematician who wrote 1500 papers, and he was traveling around the world meeting mathematicians.
He still everyone has this number So if you publish a paper with this, you have Erdos number one If you publish a paper with one of his coauthors, you have Erdos number two And this person you work with there, there's and he was a schoolteacher And then he told me, but we we met at the, at the camp and he said, young man, you have some talent for mathematics, but do you know that in mathematics there are problems that cannot be solved in three hours? In the three hours you have in a competition.
And this really made me think And this changed my perspective on mathematics From that moment onwards, I started to to solve problems But thinking that what if I change this condition? Can I generalise this result? So I was losing focus on the competitions, but then I was starting to think about research Then I nearly gave up maths.
But then I had the rebound When I was 18, I won kangaroo mathematics This was in Paris I also met, further afield I think he put he brought me like into the church.
He told me, look, you have talent, but you cannot leave mathematics, so you cannot leave mathematics. From now on, your life schedule is oxygen, glycogen, sleep max And then don't miss liturgy that Don't be horoscope That's, his advice.
But he was very sweet, sweetheart Yes And then, like, meeting in the in the classroom of, Professor Bain said So this is Professor Mihai Vinter, who is here today as well So I think Professor Benson was inspiring students because he was playing the piano.
He was playing the organ in the in the black church, in the famous church in in Russia. He was writing poems He was with cultural activities He launched many competitive match competitions He authored more than 15,000 proposed problems and more than 6000 open questions.
And we are still working with students on open questions I'll tell you more about it. But in the same room, in the when we had tuition, we had Radio button and Union State Radio decided to follow diplomacy, And he's now the current head of the liaison office, in Erbil in Iraq And Radu is also here.
And by the way, he will have a lecture He will have a lecture tomorrow showing how you can solve diplomatic issues through numbers and data science So I hope that will be interesting. And then also you initiative, he was like the genius in our high school He was going to a national competition in chemistry, physics, mathematics.
And then he studied mathematics And I insist on these two guys because you will see in the next slide You know, I don't want this presentation to be like my Instagram, where everything is perfect because my life is not simple, is not linear, and it has its ups and downs, and I have my very low, point And then I had friends who raised me up So if you raise your friends, you are doing a good job.
So, when I felt down, I had failed you here in university, and I'm happy about that My mom was not happy, but I'm happy And then these are the guys who welcomed me to their city So I changed cities They hosted me for a while until I found, like, my, my group to do mathematics.
So I was for a year in, in Bucharest, in the Polytechnic Institute We had 35, hours of, like, face to face, activities a week It was quite brutal Classes Saturday And then you had to do the labs overnight.
Many of the survivors got very far So they are leading companies We have one such survivor in the room So this is Professor Serino So he.
He's the head of the intelligence systems lab in, in Paris, actually So he survived, Polytechnic Institute He did PhD as well But I failed my first year And actually, my salvation came through research because while preparing for an exam, I found a nice problem.
And then instead of preparing for the exam, I started to solve this problem, and I thought, this is this is a way to arrange the numbers from two dimensions on a single line through an exact formula So with two variables I will not explain the proofs and so on But then my question was how can I do this in three dimensions and then add four dimensions and so on And that was my first published paper I had 100% grade equivalent for that exam.
But that was my first, my last, exam in that university And then I went to Cluj Napoca. In Cluj Napoca, I did BSc, MSC It was totally different atmosphere with mathematics I started to publish papers solving open questions from Octagon, also solving my own, my own interest I started to be interested in inequalities.
And so inequalities are actually the dominating relation in mathematics and life, so normally this is an inequality So you have x y z are three positive numbers And whatever those numbers are these this expression is greater or equal than three halves.Equality is actually a particular case of inequality.
So you have two numbers are equal If one of them is greater or equal than the other, and the other is greater or equal than the first time So equality is actually an accident But then I started to publish I had great guidance from two teachers.
One of them unfortunately passed away So let me run a code So they provided me lots of guidance, tutoring and so on And then I also met the person who really solve the equation for my like, because during faculty I was focused on mathematics, but I was also trying to solve a conflict because I was going to church I was faithful, but, I was wondering, am I not wasting my time doing mathematics? I was going to the library for six hours.
I was reading theology books Three hours I was reading math books for the remaining three hours And there was a conflict in me And then through this, this is a metropolitan, like a cardinal in the Orthodox Church And, he had, he was an engineer.
Then he studied theology, two PhDs in Jerusalem And he told me, no, no, no, you are not, you are not, doing theology Now, your way is mathematics And he told me an astronomer who discovers a new star brings a liturgy to God. This solved the equation for my life because I realised that whatever I do.
So working my talents, this is how I can be fulfilled I have a fulfilling life Then I came to the UK to do a PhD. I did my PhD in the University of Nottingham, a great applied mathematics project Stochastic receptor ligand binding under force.
So this is about how the cells, this is the process which, expresses how cells adhere to each other. This appears in many processes like morphogenetic movements, metastasis, tissue formation, wound healing I had to build a model, so we were considering that, two cells are modelled as two plates Plates, linked by some bonds.
These bonds, everything was under force And in a fluid I didn't look like this project too much Everything was non-linear I like to do formulae.
I wrote the formula for an n dimensional integral, but I could not solve it numerically. So what I had to do, I had to learn Matlab I had to learn stochastic simulations, Markov processes, discrete time space, discrete, discrete, state space, continuous time, and so on So I could do only simulations, but I ended up getting my PhD also doctor in the process Stephanie.
But, I think maybe one of the biggest achievements I realised about, about my PhD is that I could really branch to the UK academia academic tradition And this is what I'm trying now to, to, to, to promote around the world because, I had three PhD advisors This is you can you can, click on this thing and this is the this is, the, the the Mathematics Genealogy Project. So you can see who the supervisor of your supervisor wasm and then who's a supervisor and so on. And then you can trace your academic ancestry and then my main, so but I had three supervisors. One was expert in fluid mechanics, another one expert in statistics, another one expert in pharmacology, And then through all the professor Oliver Janssen, who was my main advisor and the best students in the MPP in Cambridge, I was linked to many Nobel Prize laureates So JJ Thomson, James Maxwell, then, certain Isaac Newton, then Galileo Galilei Tartaglia.
He's the one who solved the cubic equations for the first time, then the Erasmus, then Isidore of Kiev and then Gregory Palamas Gregory Palamas is one of the greatest theologians ever So I was quite happy But then in 2000 I was jobless, and after I finished my PhD Yes.
And then some I also wanted to ask you You can start now if you have some pen and paper, you can write a probability of the events happening for each light, and then you can multiply these probabilities to see what to get in the end So in 2012, in 2011, actually right in December, after, I was graduating, I get the phone call from a friend in the church Like, at that time, our priest was applying for jobs.
My friend was applying for jobs No one had the job, And then And then this friend of mine calls me He says, look, let me.
I found your job This is your job This is lecturer, Derby University This is I tell you, this is your job Then I call the priest.
I said, father, then what should I do tomorrow? You call them Then I had the meeting with, with the people in the University of Derby. I had a meeting with the head of school, with the head of subject, with the the principal tutor of the university, Stuart Berry I think many colleagues know Stuart He was here for 43 years and, I applied.
I got the job and, I became a part I had a very interesting interview That they asked me how much, how much did you earn in the previous job? And I was I was so nervous And, I wanted to say, £24k per annum And what I said was £24k per week.
And then And then Peter Larcombe was, started, took a, took a notebook and he said, which company did you work for? The then the head of school said, I'm afraid we cannot afford to pay you that much, but maybe we can sort something out and then and then I made two promises, which I am, I'm trying to keep, I, I told them that, look, I am very happy to join, I am not here for the paycheck, and I'm here to make a difference What I would like to say now, after becoming professor, is that, I do not see this as a prize as a as an award for various merit, but as an investment Right So I'm.
And I'm the investment of my parents I mean, the investment of my teachers I'm, And I'm here to help everyone raise their game Now, the first meeting, in 2012, I, we had the first meeting with, some academic team And the the topic was, what is research we were trying to define.
We did not have, charge to tell us So we were trying to define let's define what is research Is it primary research is taken We then we had the statement Yes, we are all happy with this definition.
The university had research, but it was in pockets Research was more like a curiosity So there are some people doing research that that person is doing research It was something, something interesting, but it was not very, not very common Then in 2013, again, I was here.
So I'm, you know, I'm very happy to be here as a witness to, to, to tell you that, maybe to realise together the huge improvement of the university in a very short time span because we don't have, like, 800 years of history We only have 30, 33 Right? In 2013, the Vice-Chancellor of that time, Professor John Coyne, mentioned research for the first time in a Vice-Chancellors briefing. Like staff are encouraged to do research with this…Good.
It's actually there is value in doing research, I tell you, that We went outside the room and we started to jump around the people in computing, because we were doing research. Then 2015, I have to tell you, that's why I have the picture with Cath on this slide, because, that for me, it was love at first VC briefing [sound muted].
So why? Because, Cath gave the, the message and so on. But then a colleague, asked the question and said look, what about the people who are not doing research? And, Cath’s response was, sorry, if you are not doing research, you are not an academic. And for us, for the people who are trying to get some recognition for the research we are doing, that was a massive boost. And now I also want, so there are colleagues who are focused on teaching. So I think that's brilliant.
But I think even in that case you can still do some research because you get a lot of data from your students. You can do reflective research, right You can reflect on your practice, what went right, what went wrong You can get research out of that.
So, I'll show you how I've done this also with my students. And then 2020 we had REF and I was very happy to contribute to the REF submission of U11 because it was, REF how is that transfer season? We lost two, two professors, through transfer, one professor through illness and so on So we did not have too many people to pick up the submission, and we were sitting on a goldmine because I was able to witness I stayed here for the whole period, and I knew that we had papers in nature I knew that we had papers in frontiers of computer science, brilliant papers.
But those were we did not have like a clear understanding of the value And then I stayed like for a month with, with the security guys They were asking me, when you go home I said, when you go home So that was like midnight.
But then we were able to get like all the data in good shape for the REF submission for U11, we selected our 43 outputs and we had 279 average out of four, the second highest in the university, two percentage two like we so 0.002 The first one was 281. So I think now the university started to submit big bids We, I think we recruit brilliant staff and I'm sure the next draft would be even better So I was very happy to be part of this journey.
But this also had an impact because we did not have a submission in mathematics, So this means that I had to adapt my research so that I can be part of this submission as well. I started as a pure mathematician then, because I was doing I was trying to help my students I started to get interest in maths anxiety, This is the fear of mathematics.
Frica de mathematica. This frica de Mathematica, And then I realised that we had world leading expertise in our university. So we had David Sheffield, we had Tom Hunt, who were leading experts. So I could identify through this interest some other pockets of excellence in the university.
So this is why my research is fundamental, research I applied, research and then pedagogical research now, so to help my students, I started with this class computational mathematics. I started by preparing the best resources I could, So I produced the textbook.I started to use recordings as soon as they became available through Panopto, I started to use maths jokes inspired by my teacher in high school, But then I started to focus on E-Assessment as well, to help all the students, to help the students practice and then numeracy skills training and so on. This allowed me to present at many conferences.
I think we had very good results in in mathematics in the National Student survey I started to do Erasmus visits, and also I started to, to bring companies, to the university so that we get the latest technology in the classroom.
This can be dangerous because if you draw the attention of, senior people, then you will get jobs as well. So I had the big job from Warren, who was a professor Warren Manning at that time the Dean of our college And he said, you will do the TEF submission form. You are the person to do it.
Come and explain what this is about. And I think, yes, we did, we did, we did Well And then in 2020, I became senior fellow of the Higher Education Academy And again, this was I think this really crystallized my key direction.
So first was internationalisation in higher education. So this is university students and staff traveling abroad, but also internationalisation at home. So through Erasmus we were able to bring some of the leading experts in Derby and then also technology and mathematical education. And I've seen that, for example, with, with E-Assessment This is how I could deal with students, with 150 students in my classroom.
And then by deploying formative assessment, the students could, lower their anxiety because they could practice the tests and fail as part of, And this became part of the learning process.
Working in partnership with the students, I think this was a big lesson for me, so I started to listen to the students’ voice, I started to engage.
My first feedback was not great I tell you, I was not in this room, but, in my after my first lectures, I said, look, the students were very quiet I said, maybe something is not going right. And I said, look, I will explore this myself I will tell the students, look, I really care about your feedback.
Tell me exactly what you think. I was not ready to hear that. They said that I had feedback or video, moves and speaks like a potato. But then after, I took action and after I started to learn from this because, students satisfaction with feedback in computing modules was often in 40%, 50%.
So I thought, look, I should engage with the students to see early on what what do they want? I should tell them a little bit about feedback. So what this feedback? And then, I had the feedback, at the end of the year was as a result of our feedback of it, you became a much better lecturer. So that's why I was able to tell you the one before Right.
And this is during Covid. Covid was a very interesting period, I think, for all of us. So during the lecture, suddenly someone pops a link into the chat box, and then all students could get this. And this was this was, this was the student, Frederico. You will see him in the following slides.
So this was his reflection He was, in the CEL, so in the centre of excellence in learning and teaching, And this was his reflection of how effective the tools he saw in the in his classroom were on his learning.
But then inspired by this, I said, oh, Frederico. Okay, good Now you go with Erasmus We have a conference in Portugal, you are going to reflect more on this thing, work with the students What went well? What did not go well.
And then you are going to present your findings at the Conference. So this is this is Frederico. He was a student ambassador, and you'll see him more. Then something that had direct impact on the students at Derby was the visit of my teacher from, from Cluj Napoca. This was a genius teacher who was working with Maple, with the company to help them improve their algorithms So he knew, like Grobner Basis, he knew lots of very advanced mathematics to improve the algorithm.
But he came and he gave a lecture on how you can use Maple Software to solve research, teaching and all sorts of things And then I contacted Maple and I said, can we have some licenses? Can we do some trial with, with Maple? Then we started a pilot project that went really well. Then we had the site license, then we had access to their books, we had the partnership, and then they started to have sessions for our students only.
So we had like, tailored sessions. Then I followed the same approach with Digital Ed. So this is, they were the producers of Mobius, and then because, so some of these tools were deployed after we had the meeting in the college in 2018. We had high failure rate in maths-heavy engineering modules. This was a problem, so pass rate was maybe 40%.
And then I was invited because pass rates in my module were 85%, where I had the assessment and all these tools. And one measure adopted was deploying Mobius. We have a colleague, George Dixon, and then when he deployed that in one year, pass rates went up significantly. Then I was invited to online seminars to discuss whether STEM can be taught online. It was Covid So I said, now we have to.
So anyway, so then, this is a book, I started to read in the night before my interview at Derby.
And actually, this really changed my perspective on my value. I thought I would get the answers to the interview questions, but I got something more valuable, and that was that every employer is looking for the same skills and this is problem solving skills. And then I realised, actually I'm a mathematician I am a problem solver.
So problem solving is about understanding the problem, making a plan, implementing the plan, revising and so on. And like this is my creed for education. I think educating the mind without educating the heart is not education at all. So this is what Aristotle was saying, and I really think that I believe that, education’s purpose is to replace an empty mind with an open one.
Now, in order to to develop, problem solving culture at our university, for my first semester, I started to do maths competitions. Then quickly, we realised that this is not really the way to go, like single, like individual competition, We started to have, team competitions this went really well.
We had 14 editions My colleague Nicholas Korpelainen started to lead on all these developments, and then in order to improve student satisfaction, we also joined the choir And I think this really this really made the difference.
And actually the first time I met the Vice Chancellor was not through, like booking a private meeting and so on But, I met, Cath in this, in this event. So she was always attending this choir, the university choir. We had a carols concert, the graduation ceremony concert And, this is when I remember that first time when Cath approached me, she told me, you are doing a good job.
You are making a difference in your team, I felt how would she know? Because I never I never interacted, but she was aware of what what we were doing. Then we started to organize maths events So, I heard that this was, Colm Mulcahy.
He was like, he was a math-magician He had a UK tour like Madonna, and he was going to, like many like Cambridge, Leeds, Birmingham, Manchester and so on. And then I dropped him, I saw that he had a pause, he had the break in his schedule and I said, Colm, hello, professor Could you please come to visit Derby as well? And he said actually I'm visiting a friend nearby.
And then we organised an event in the big lecture theatre with math magic. And again, what is the impact? So I don't want to just provide like a list of things that I've done And you say, yes, good You work very hard, but I want, I want, I want to show the impact these things had on, on our open days. Because we started to do math magic. Then we have students who are now leading the, the, the, the magicians activities like math magic in Derby.
So we have Tim Green who's now working also in course And, like this thing really left the trace. Then, careers events with the maths twist, so we had Ashley, so Ashley was senior operational research analyst at the Department for Work and Pensions, and he was joined by one of our graduates I realised, that so building, a placement visit, I had so I went to Newcastle to visit the student.
And on the way back, I met professor Tom Ward, who joined us today as well. He's like my mentor for mathematics in the UK He was Provost for education And, he kindly, he kindly showed me around in terms of the facilities they had. And the one thing that stood out was the visit to the, the alumni office, and that had about 17 staff.
When I came back to Derby, that was 2015/16, I asked my head of department, what alumni office do we have? Because we have like all these great stories, we want to keep in touch with the students. He told me that at that time we had someone, he remembered having someone part time. Now I know that we have a team and we are now working with colleagues in data science to help get the data on our alumni to really keep in touch with our students. And then we also organised, in 2018, a public lecture with one of the greatest mathematicians alive.
So this is Preda Mihailescu, very interesting life story He's also Romanian, but he's the one who solved Catalans conjecture. That was an open problem in mathematics for 158 years, And then he's the one who solved this problem And then he came to Derby to speak to our students.
His talk was called with mathematics on the road. So this is what inspired me to choose the title for my talk as well. But then, we were using all these events as training opportunities for our maths ambassadors. One problem that we faced in Derby was that the Maths team has always been small. At some point it was only two persons.
We were getting lots of invitations from local schools Can you come to speak to our students? We want to have some activities and, we had to reject many of them And I realised, yes, we should not reject all these things because we don't have too many staff, but we have lots of good students And then we can train the students We can deploy them to local schools.
Then we realised that we had a fantastic widening access team, Schools liaison officers, and then through DANCOP, through Raising the Grade, we were able to deploy all these Derby students to local schools to help teachers, to help with raising the grade. This was an event that this year and this was, with 500 students and it was our Derby ambassadors, all with Maths at Derby T-shirts helping them. Then Staff Experience with Erasmus Plus, here I have some pictures with the colleagues in engineering. So we have team.
We have Mark, so in the morning we had the research visit, in the afternoon we were in the jury for the national engineering competition for students. Then we had the graduation ceremony Mark was enjoying, papanasi, but this is a very traditional dessert. Then with Tom Hunt on maths anxiety, visits to Turkey, visits from Turkey.
So So why is this important? Why were we doing this?, during this visit So I remember that when we went to Turkey we met the vice chancellor.
Then we went to schools and we could see that in Turkey, they were doing research not only on the students anxiety, but also on the teacher anxiety We could see the problems faced by the teachers teaching refugees. And they were saying that we had an Afghan refugee child, and he slapped one colleague and then waiting with the parents at the gate, Right. And then we could exchange experience to say, look, life is complicated for those people.
And we can learn from that experience And then this is the last Erasmus visit, unfortunately So due to Brexit, we had to change plans But I was very happy to take, Stephane to take, Farid to take, Harry to Alba Lulia, we have great partners and to Cluj Napoca where we also have great partners.
And here I would like to highlight the doctor Gian Luciano Popa So he's same age as me. We met when we were both young lecturers, energetic. We exchanged visits, regularly And then through these, visits, we're able to plan conferences, papers, grant applications and so on.
He's now the vice, president of the university dealing with international relations and still a good friend of the university. Since 2022 We started to have Turing, scheme So this replaced Erasmus And this means that we were able to get to see some of the, I think, most active research labs in the world This is Professor
Come in So you see him here You see him here. He has a lab with 35 students at all times, then postdocs. The place has I think 30 events every year Workshops, symposium where he is doing internationalisation at home He brings the leading experts in, AI now So he started with fixed point theory convexity.
And this is the training he provides. He selects the best students from Pakistan, from Ethiopia, from Nigeria, from all around the world. He brings them to this lab and you will see some of them visiting us. So we also had many guests at the University We have the guests with Erasmus from Alba Lulia.
Here we have, Warren greeting, Professor from University. This was the first ever Key Action 107 application of the university So this was Erasmus partnership outside Europe, €90,000. It was great, but we could not start because of Covid. So the first visit was due to take place in June.
Then we had Professor Subrata from Jadavpur, the first visit by Anand and Graham or put so this is the the lead, the leaders from Britain. They visited the university in 2018 for the first time and then we had guests from Thailand So this is Professor Tanakit and Professor Kasamsuk with their PhD students now, and also Professor Poo, with some collaborators. And then actually, you've seen already some of my research before this session because, this picture was selected for the Strategic Framework document of the University, I'll tell you what these things are in the next slide.
This was another visit by five students, another visit by, And this is the first visit that we had from Thailand. He he's, he was from Ethiopia finishing PhD in, in King Mongkut University in Bangkok. Now, what is what links the two PhD students, the two PhD research visitors and the ones on this slide is that these visits took place two, three years ago Now they are already lecturers in their universities and they have Derby in their CV.
So Derby became part of their journey as well. Yes And I love graduation ceremonies. Now this is another unique experience we provide to our visiting students. I would like I wanted to start with this, but I'd like to really thank, the events team, marketing team.
It's like whenever we go to these graduation ceremonies and I think if you take away something from today, So I would really invite all staff, to join these graduation ceremonies I think they’re fantastic. And it's a unique occasion to celebrate our students and also to realise the huge, work behind the operation of our university.
So I always enjoy to have a photo with this colleague from security, because I know that he's there and guarding the university. And then and then these gentlemen seemed very familiar at the last graduation ceremony And actually, I realised that we met at the training course that we did, where we did maths training for, for, the Bosnia Herzegovina community. This is a partnership program lead for China. We have, now we started this program in 2022 We already have three cohorts of students, with over 330 students.
This is from, a picture taken during our visit in October 2023. Now, I'm joined by a team of excellent academics And, I know that some students in this room are very interested about the Turing Scheme applications. So this year, we are going to have, for the first time for Turing scheme, placements in China. So we are going to take the students with us and also Turing Scheme placements in Thailand. So I'll come back with information. On the 4th of February We have the training. Finally I talked about, lots of things But now let's go back to Maths.
So you relaxed enough. So Roger Bacon was saying that maths is that the key and the door to the sciences. And Galileo Galilei was saying that this is the language of the universe. Now, maths has, significant emotional impact, So Martin Luther was saying that medicine makes people ill, mathematics makes them sad, and theology makes them sinful. And then a line, a line I use in my open days. Or like opening, inaugural lectures with a course Is this one from Albert Einstein. He was saying that do not worry about your math problems Mine are far greater. So And then my understanding is that if Einstein had problems with his maths, then it's okay for me also to struggle from time to time.
And Sofia Kovalevskaya was saying that it is impossible to be a mathematician without also having the soul of a poet as well, because you will see that some of the maths is poetry. Now, how big is mathematics? You encounter so much up to all levels, so you get like geometry, algebra, some calculus, some statistics. Right now in university you find out that there is functional analysis Calculus is not It is not just calculus.
It's one, two, three, four and so on, differential geometry and so on And applied mathematics. But if you check the mathematics subject classification, there are about 5000 fields in mathematics. I remember that I was, almost crushed when I entered the maths library, in Cluj Napoca And then after I opened the door, I've seen, like the shelf, which was like six meters high, six meters tall, and then very long.
And I thought, I will never have time in my life to read, maybe just this shelf, but, yeah, maths is big, right? We have many numbers in mathematics and numbers it only appear quite late, actually, in history. And I want you to use the example of number Pi. So this number pi you divide the circumference of a circle by the diameter And there are many approximations now since antiquity, but only in 1760 Lambert proved that this number is irrational.
So the digits do not repeat and they cannot be predicted. So we have these numbers, natural numbers, Then if you take with plus minus sign, you have whole numbers. Then if you take fractions you have rational Then here the last layer is real numbers.
So this means including e rational, So this is pi, e and so on. Now if you don't like math you can also think of this pi.
Yeah So that's that's fine too. Now about about infinity. So this concept of infinity bothered many minds right Because it's like if it's if you have something that, if you have 100 people in this room, so you count up to 100, how do we know that there are 100 people in this room? What would we do? We would start to count, right? So we would say one, two, three, four, five.
So this means that And then when we finish this is the number of elements in this set. So what we actually do when when we say the size of a finite set is we establish a 1 to 1 correspondence between the numbers, between the the first element and the last element Right. So if according to Big Bang, there is I'm not sure if you find infinite infinity in the universe, because an estimation of the number of atoms is 10 to 8 2 max.
You can put that to power ten 100 Then you get something bigger. But, this infinity has, has many interesting properties. So if you take the numbers starting from zero, so zero, one, two, three, four and then the number starting from one, so apparently so you actually delete the first term.
Right So which of the two sets has more elements? I say if you have 100 people in this room and you take one out, you have less elements, but with infinity it’s different, because if you if you take this process and you attach to every number in the first set, correspondent in the second set, if you can do this without leaving any number outside, then the two sets have the same number of elements, right? So even if you delete 1000 elements from an infinite set, you still have the same number of elements that you had as you had at the start. Same thing applies to division So if you take the numbers one, two, three, four and then you, you only take the even numbers, they still remain the same. So if you take an infinite set, you divide it in two parts.
Each of the parts has the same cardinal as the There's the set at the start. And, trying to understand infinity There was a mathematician in the 19th century, G. Cantor, who had the following idea.
So when you think of the fractions between 0 and 1, you have one half, one third, one fourth.
So you have infinitely many fractions between 2 and 3 infinitely many fractions. And Cantor had the idea how many fractions are there And then his, his genius idea was that he could arrange actually these fractions in a table, and then if you go through these, if you visit these fractions in this way, like a spiral So you are going along these, these, these arrows, then you can establish a 1 to 1 correspondence between the fractions and the natural numbers.
And this means that they have the same number of elements. So between 0 and 1 you have infinitely many numbers between 2 and 3 infinitely many, But still the fractions are exactly the same number. Then also Cantor had tried to count how many real numbers are there, and then skipping the proof, but he proved that this is a totally different type of infinity. An infinity much bigger.
So this is an uncountable infinity. So and then he also developed the theory which shows that actually infinity is infinitely diverse. So my mind was actually right with the infinity of infinity, infinite. Then another interesting concept, that fascinates me is dimension. So a point, if you are at a point, you don't move in any direction, so you have dimension zero.
If you have a line, you can move in one direction, so that's dimension one. If you have, if you have a square you can move in two direction, So that's dimension two cubed dimension three, and so on. But in maths you can go on.
So you can have four dimensions But you can also have infinitely many dimensions Then an experiment done in 1960s by Mandelbrot, tried to measure the length of the UK coastline And then when he used rods of 200km, he was getting 2350km But when he used rods of 100km, the length was bigger.
When he had, the rods of 50km, this was increasing even further. And he reached to the idea of fractal. So I just go very quickly through this, through this concept using the example of the surface key triangle. So you start with the full triangle You take the midpoints of the sides.
This divides the initial triangle into four equal triangles, and then you extract the one in the middle, so you get three out of the four full triangles. But you also draw three new lines three new sides. You can quickly check that the the area of the new object is three quarters of the, of the original, but the perimeter is three halves of the times the original.
The original if you keep iterating, so if you apply this process over and over again, what you get is that you you create an object. So through this mathematical iteration you create an object which has infinite perimeter and zero area. So what is the dimension? Infinite perimeter means the dimension is greater than one zero area, dimension less than two. So mathematicians had to come up with a theory to explain what is going on.
And this was the Hausdorff dimension, one of the dimension concept, which shows estimates that this dimension is 1.58. Now this type of object is very useful in computer graphics because this means that you can you can give the impression of some, field spaces using little amounts of information, then Fibonacci numbers we could not have, like a maths generic maths presentation without the Fibonacci numbers. So these are the numbers zero, one, one, two, three, four The rule is that you add two numbers to get the next you start from zero and one These numbers were published in Liber Abaci by Leonardo Pisano, also called Fibonacci, but these numbers appear in nature.
They appear in music, they appear in many patterns for example, if you want to find the optimal shape of a concentrated solar power plant, this was the shape which is linked to the Fermat spiral, which is based on Fibonacci. Now there is research showing that, these Fibonacci numbers were found in India in around 400 BC So maybe these are not Fibonacci numbers. So if you are interested in the decolonisation of mathematics, I think this is a powerful example.
So like Pythagoras theorem, like all these things that we attached to someone, maybe they were just more popular, but maybe it's not their concept. Now this is the power of mathematics So yes, you can compute these numbers per second and so on But the power of mathematics is that it can give you a formula with which you can generate any of those numbers, also infinite sums. So if you have like this, the sequences where this, this, so the sequence was the list of numbers never ending.
But you can also have infinite sums. And what's interesting is that these infinite sums, you can have infinite sum of positive numbers which has finite sum, and this is, like the more mathematics, you know, the more jokes you can understand. This is a calculus joke So it's like infinitely many mathematicians walk into a bar the first night, says, I'll have a beer.
The second one says, I'll have half of a beer, the next one says, I'll have a quarter of a beer So every time you get a half of what the previous one had, and then the barman puts the two beers on the table, and then mathematicians say, so are you joking? Is this, is this correct? And the bartender says, come on, guys, know your limits.
So the joke is that if you add the half. So if you use this unit square, you have a half a quarter, an eighth, a 16th And then when you add all these numbers, you get one. So that's the proof without words. Then complex numbers. so these are important for the following slides So we have the real numbers.
But in real numbers you cannot solve some equations If you take the if you take the quadratic x square plus one and you plot the graph only for real numbers, this curve will always sit above the horizontal axis. So you don't have a solution. But mathematicians needed to solve this equation, so they said okay, we take x square.
We take one on the other side x equals minus one, We take the square root and we denote this. This is I. This is the imaginary number. And then these numbers are numbers in two dimensions. So they had real part horizontally and the imaginary part vertically.
This leads also to the most beautiful formula in mathematics, So Richard Feynman and others Said that this is the most beautiful. It helps us to understand more jokes So life is complex because it has real and imaginary components and also by conversation between pi and I get real, be rational and also material for open days because, marketing was not very fond of this.
But but maths applicants were very excited about it and also by visitors I brought them to the open day.And then the professor was saying, make it complex, professor Make it complex. Yes Let me cross this because complex numbers are the next level.
And then, There is a famous work by Paul Erdos that the mathematician is the machine turning coffee into theorems, and this is exactly what happened with me at Derby. So in my second week, as a Derby academic, I had the coffee with Professor Peter Larcombe, who showed me some sequences. These were sequences like Fibonacci numbers, but in two dimensions and, he showed me that sometimes these, so you have patterns with 12 terms only, and these patterns were self-repeating.
And he asked me, can you find the proof? So when does this property happen? And then I was able to find the proof to do many simulations. He was actually re-igniting some research left open by a Horadam started in 1960s. Then we were able to characterize the periodic sequences. That was the first paper in Fibonacci Quarterly that was 50 years old, the journal.
Then we are able to enumerate these patterns using combinatorics, and that was another paper. And what do you do with your research? Then you start to show it around the world And we started with, British Combinatorial Colloquium. After my presentation, I had an invitation to give an invited lecture to Open University.
So we did that And then I presented at, the interdisciplinary, Forum of Babeș-Bolyai University, of my presentation on the mathematics of beauty. The other presenter was a psychologist, who is now the Minister of Education in Romania. Then we started to advance this research more, we started to look at non periodic sequences as well.
We were able to design a new random number generator And this was the basis for my second PhD in Cluj Napoca, where Professor Tom Hunt was was my external examiner and actually he was the author of the main textbook in recurrent sequences in 2003. And, I think this quote is very relevant for this presentation, because Dijkstra was saying that the picture may be worth a thousand words, but the formula is worth a thousand pictures. Because all these formulas are obtained from all these pictures are generated by a single formula with changing some parameters.
And then, next year we made it to the top because we submitted this research to the International Congress of Mathematicians. This was the forum where the Fields Medals, like the Nobel Prize for mathematics, is awarded. And we had 5500 mathematicians from all over, all around the world, about 90 from UK and one was from Derby. So after I made it here, I was getting angry whenever I was, hearing from colleagues, you know, we are not very good with research because we are Ferby I said, what do you mean? I mean, I presented Derby research at this forum, so I was able to present the research.
I was able to meet the Prfoessor Dong Hwa Kim for who was writing emotions into equations, working with KIA, and they were telling that actually Korean cars were so successful because they had mathematical models for modelling the client expectations. Right Embedding those in their car designs was making the cars, sell. And then here I also met, here we were dressed in prime minister and Korean king with the professor Raja from India And then, this became one of my leading collaborators.
Now, starting from conversations with the my colleague Stuart Berry So, Stuart, was at the university for 40 years, he was not publishing much But if you had any problem, he was able to to build a heuristic, a code in 12 pages, 15 pages and so on That worked. And he was able to solve where to place speakers in a concert venue using some simulated annealing table search.
He was able to do that, scheduling for time tables, trains and so on And he was able to do that. And then he showed us a problem about traffic assignment So you have a number of routes between an origin and the destination, and you want to push 1000 cars. You have a certain cost of sending the cars along each of the different options, and you had to find the social optimum, which is the minimum travel cost overall.
But, normally drivers choose what's best for them And this means that you have traffic jams. So this is equilibrium solution. And then for this problem we started to explore different versions of the equilibrium problems, different versions of optimal problems, and we start we had the first and you have like the, the price of anarchy and so on. So this is a very important concept.
But in 2017, this colleague invited me to India The conference was during teaching time. I never left Derby during teaching time before that And, I asked my this was my first invitation as a keynote speaker class.
My manager, he agreed I don't know how, but I was very happy. And then I was able to give a keynote presentation But, I spoke to our international team They asked me, have you seen any students? I said, yes, I've seen 450 students.
It was a great experience, and I was also invited to inaugurate a research, centre for mathematics. And, that was, like, off the schedule, but then last summer, they called me and they said, you remember when you came to this inauguration? Now we have 12 students from that centre. Then this collaboration led to REF papers, visits by another collaborator, Professor Popovich.
Yeah, I will skip this maths You can close your eyes I'll tell you when it's not maths anymore. But I started to do research with Professor Nikolai Popovich on generalised convexity. And this led to invitations to present at the biggest operations research forum in the United States. So this was 6,000 participants.
Then I started to work with Professor Andrica on partitions with partitions of multi sets with equal sums. This paper is it is important because, for example, if you want to send packages, data packages, along multiple channels, if you want to have perfect balance, how many configurations are possible? And then only November we found out that there is a paper citing us, actually we built the theory for this. There was only theory for sending all these data along two channels.
But we did the theory from from scratch for k channels, and then they applied this problem to solve, to find the, to construct and enumerate all the balanced rotations, symmetric Boolean functions, opening and closing an open problem in cryptography which was open for 20 years. So that was one thing the cyclotomic polynomials You have nice formulae about the poetry.
But also very nice marketing materials. So you have seen these photos already, then dynamic geometry. So we did we did a fair bit of maths And this dynamic geometry, took us far away. We had an invitation from ICDEA.
This was a conference organised in Paris by Professor Sorin Olaru, and we had an invitation to organise a special session, And I presented our research it was very received. The session was successful, but I had this photo, and I've seen that there is, there was a gentleman, approaching me I was showing off my, I love maths badge.
And then during this photo, this person said, you know, I'm the new president of the IMA. We make these badges, I'm the boss here. So this was Professor Paul Glendinning.
Then the quick I'll just go very quickly through some applied research So, placement visits This can be very tiring for staff.
So you have to go travel long distance and so on But I was fortunate to visit Luke, and Luke was the assistant of the operations manager of a huge warehouse. Then with him, we discussed about how to optimise the operations because they have 1000 pickers, so you could plan better the routing across the warehouse that was as big as seven football pitches, And then I followed his career, and he's now DHL fleet controller for DHL.
So he applied the skills developed here. Then another item of applied research is ceramic colour models. This was a project where we were helping a company improve the process of designing new ceramic colours. So they had to identify which pigments and which concentrations, and we won grants.
We improved the process, but the heroes of this project for me were our Derby students. And then through URSS, through Erasmus, we were able to contribute And now they are both doing PhD. Another highlight for this session is, Craig, I'm very happy that Craig is, is, here.
So Craig, was doing, so he was a Derby graduate, but many, many years before. I had the presentation in his school, he was a maths teacher at Bilborough College, a Nottingham College. Yes And then we told him I told him, look, we are launching a new MSC in, in computational mathematics. He was the only student that year, but he was a brilliant student, then he did a PhD and then he worked in London on very good money, I know.
But now he's a research fellow in machine learning. Yes And then, and also his PhD was on the Alice CERN project, and it's the only PhD I know, I know about in my experience, where there are no corrections. So I think that's quite, quite impressive.
Then we had many, many successes, so I tried to reduce the number of slides. So we had many successful, so I tried to really put everything. So we had Claire Barratt, I'll just use a few seconds for each slide.
So Claire Barratt was doing aplacement with IBM then, she is now senior solutions architect. At this project with our Derby students came in the top ten in the world in the IBM Global Challenge. And this project was led by my colleague Rich Collins So he was the advisor for these three students.
And I think they did an amazing job, but then they came back to Derby for when we had the first enhancement week. She was one of the speakers for our students Then we did research on mafia networks. We got our hands on data from Sicilian Mafia investigations of the European police.
And then we were able to reconstruct meeting. the networks of the meetings and the phone calls between mafia members And then we were able to build mathematical models to tell law enforcement agencies which are the most dangerous criminals, not only in terms of connections, but also in terms of influence. So we had many, many, researchers in the team. Lucia Cavallero led the project, and then she did postdoc, and now she's a very successful lecturer And then we presented this research.
So it was all over the European press, And also I presented in Ethiopia, then I was invited by London Mathematical by, I had funding from London Mathematical Society to, to do some workshops. Then Encyclopedia of Integer Sequences So we don't only have Fibonacci, we have almost 400,000 sequences And I just want to tell you that some Derby students have their own sequences as well. So I think that's very exciting.
And then we also had a maths conference at the university. We had Professor Tom Ward, Professor Preda Mihăilescu, Professor Martin Bohner.
And then how do you involve your students with research? So my message from, from the slides is that there is research of different levels, so there is research, pedagogic research, there is technical research.
So we had many students who got involved with this symposium on mathematical education in the European context, and then they did very well in their careers. This is a Derby student, this was the first Derby student to go abroad with Erasmus And then she won the URSS Award.
She gave the vote of thanks But then she's now working for the Met Office. And then we also do, research in AI for education, research on the impact of numeracy training courses on our students, And this was the research conference in Portugal So here we have David, Max and Damon also.
And, this is Socrates, and he's the lead of the AI in education research group And I can tell you that one of the biggest assets of this university are the mature students. So we had David, he developed a derby GPT like a version to help the students And this was, the feedback provided by the GPT itself.
And it was saying that, look, you can get advice on how to survive or reduce maths jokes. This is where you can ask for help. And then we did many activities with Black History Month So we had students to promote and this is the that was the president of the IMA.
So he solicited that Then we had other research conferences where our students built a new board game in a suitcase, And this was very well received by the participants of the conference, And this was a paper published, you know, open education studies. Then we are working closely with the Romanian community as well.
So I had an award for supporting the community throughout the Covid pandemic. We have, a society within the Nottinghamshire Police. This is father Dan that was running around the whole area And, this is one of the, I think, excellent Derby graduates. He's a graduate from law, but he's a member of our community, and he is now District Crown Prosecutor.
He was the top law student in his year. He graduated in 2018 And now he's already District Crown prosecutor in the magistrate’s court. This is the applied mathematics I had to solve this month. Normally, so in our parish we had 300 locations we had to visit, across 12 cities Father Dan is the main, project lead for this.
So he has to visit, this is the map for Derby, and this is an application of the vehicle routing problem. So we have to solve this.
It's not I will now just speak very quickly about, maths support So I think it's critical to get maths support right. This improves university KPIs overall And we should again mature students I want to highlight here This is Natalie Bailey.
So she was a senior fellow in Cambridge, and for family reasons she decided to study maths at Derby, And she was the energy between setting up a maths channel for the, the channel for the maths society. We interviewed the president of the IMA. We interviewed, we still post many videos to help the students learn mathematics.
And then when I started to prepare the tape submission format, I realised that actually we had the like in terms of math support I was not starting actually thinking myself. We had the history of 30 years of doing that very well, snd through interactions with Professor Graham, what, what I came across was this numeracy gap problem. So there is a big issue in our society.
My focus was maths anxiety, I was thinking that the fear of maths is the problem But he told me, no, I don't think that this is the biggest problem. The bigger problem is that, about 16% of students do A-levels for maths, but, nothing is done for the others.
And I think we need to, to fill this numeracy gap, and I think at Derby, in collaboration with Vretta, we were able to build a solid partnership to develop a solution for filling the numeracy gap. We helped them transform their technology with topics, with dashboards, with the new courses developed in collaboration with colleagues from across the University. This made lots of, students revise and get to terms with their maths. It had profound impact in my classroom, so it helped students get their pass rate, So the pass rate in my module went up from 85% to 90%.
That's a huge improvement But in terms of good grades, this went from 60% to 70%. We had digital badges, we have now pedagogic research with the data from these modules running in Greece and China as well. We started to to train the communities as well.
We had Romania community, Bosnia Herzegovina community, SADACCA community. This was a program, sponsored by the European Social Fund And this one was the award for the best summative, assessment project. Thank you.
Professor Ovidiu Bagdasar's Inaugural Lecture 'A Mathematical Journey: From Infinites and Fractals, to Real-world Applications' video
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