IB Maths Tutor & Lecturer; Holds a Ph.D. in Math with vast tutoring experience!
IB Maths Tutor & Lecturer; Holds a Ph.D. in Math with vast tutoring experience!
I tutor mathematics and statistics at all levels, from middle school to master's level. Still, I focus on A level, IB, and A level further mathematics, among other equivalent mathematics curricula.
Research in high dimensional statistics and machine learning, specifically high dimensional nearest neighbor search problems, using a concentration of measure and random matrices. Two research preprints.
Music and speech detection (coding in Python and TensorFlow): Developed a kernelized SVM classifier that can classify music and speech with 98% accuracy using the MFCC features of the audios and used it to segment recorded call audios into music and speech. Also developed a long short term memory (LSTM) classifier that gave 95% accuracy on similar data.
Image classification by their projections and shape difference matrices (coding in MATLAB and Python): Applied support vector machines (SVM) and linear discriminant analysis (LDA) to the HOG features of 2D projections from 4 different camera angles of 3D images of human and non-human data, and initially obtained 98% test accuracy. Since a number of HOG features (1764) here exceeded the number of samples (1524), we perform regularized LDA to select the best 588 features, and still obtain 95% test accuracy, with the model, not overfitting.
Classification of fetal alcohol syndrome patients (coding in MATLAB): Performed linear discriminant analysis (LDA) on 175 precentral and central sulcal curves, with a 120-dimensional feature space consisting of Fourier coefficients. Estimated the performance of this classifier by 10-fold cross-validation to obtain classification accuracy of 76%.
Development of a new mixed effect longitudinal model for Alzheimer's disease modeling (coding in MATLAB): Developed a new mixed effect longitudinal model on shape spaces relevant to medical imaging and computer vision, using the geometric concept of parallel transport, that compares time-series trajectories with different onsets. I developed and implemented an algorithm to estimate parallel transport with error rate O(1/number of steps), showed the error rate is the best achievable and also has a smaller error compared to Schild's ladder algorithm, previously used to compute parallel transport.
Doctorate (Ph.D.) in Mathematics
Master of Science in Applied Mathematics
I think teaching and tutoring are in general collaborative processes. This means both sides must do their parts to make sure that the student gets the concepts at the end and secure good grades. The teacher or tutor must take responsibility to explain the topics that the student is struggling with, and the student must do their parts to make sure that (s)he tried her or his very best to get deep into the concept. Besides, I think mathematics teaching often lacks real-life examples. This is an issue I work on while explaining a new concept to my students and the issue gets more prominent as the level of the math involved goes up. For example, it's plain to give real-life examples of the addition of two fractions, but not so easy to give real-life examples of vector valued random variables, which requires knowledge of the corresponding areas where random vectors are used often. Having worked in the highest level of mathematics, both in pure areas (Ph.D.) and applied areas (industry), I'm very qualified in real-life motivation. Lastly, I believe that math tutoring should incorporate lots of charts, diagrams, and figures to make abstract concepts visually appealing to the students. For example, such figures are necessary to explain concepts like conditional probability or mechanics. Thus I make sure that the students are at ease with the topics by drawing them a lot of such diagrams and figures.
The first lesson will focus on figuring out a lesson plan, and regular schedule so that we stick to it in the future and also that I'm aware of the student's biggest weaknesses, so that we can return to them as we go on with the lessons. The first lesson also gives me an idea of how hard the student is willing to work, and how much (s)he already knows of the syllabus. I've had students who were already familiar with significant parts of the course materials, but I also had students who saw all many kinds of stuff derived in class before them but didn't really understand much of it. Thus the first lesson serves many purposes simultaneously. Of course, if the first lesson is longer than one hour, we do end up solving some problems or discussing some theoretical concepts.
My effective visualization process helps my students to be able to remember the formulas not as they are but by a figure. Besides, I often derive the most basic formulas in front of the students to make sure that they understand the derivation as well. Once they understand the derivation, remembering the formulas they're deriving becomes very easy. For example, I've noticed that most students can't remember a change of variable formula for integration, so when I derive it from the product rule of differentiation, they see that the change of variable formula is nothing but the integral calculus version of the product rule of differential calculus. And this is merely one example, another could be to derive many trigonometric identities one from another, without appealing to any other external formulas. When the students can remember the formula without any external help, they take yet another step towards independence.
I never stop giving real-life examples to students. Even if the student is pursuing AA (Analysis and Approaches), I often connect the abstract theory to their interpretations in real life. This way the students learn that what they're learning will be used at some later point in life, and hence find true meaning in learning the concepts. This makes the students motivated.
I first give her/him a problem, if (s)he fails to solve it, I give her/him an easier problem. If she does this easier problem correctly, I try to study with her/him how far the solution to the easier problem can be applied to the initial, more difficult problem. This lets me and the student know where exactly is the first step the student got stuck or did something wrong in the initial problem. Next, I go back to that step and go through its theory and then finally come back to the initial problem using that theory. But most of the time, the student is able to solve the initial problem on her/his own, when (s)he is subjected to this method of learning.
Developing reading comprehension skills is incredibly important for growing readers, starting as early as picture books. As children get older, it will help them understand textbooks, newspapers, and other more complex texts. Here are some steps I take with my students with difficulties in reading comprehension: Have them read some of the concepts aloud. This encourages them to go slower, which gives them more time to process what they read and in turn improves reading comprehension. Plus, they're not only seeing the words — they're hearing them, too! You can also take turns reading aloud. Provide math books at the right level. Make sure the student gets lots of practice reading books that aren't too hard. They should recognize at least 90 percent of the words without any help. Stopping any more often than that to figure out a word makes it tough for kids to focus on the overall meaning of the story. Reread to build fluency. To gain meaning from text and encourage reading comprehension, the student needs to read quickly and smoothly — a skill known as fluency. 4.If your student is struggling with reading comprehension, they may need more help with building their vocabulary or practicing phonics skills. Supplement their class reading. If the student's class is studying a particular theme, look for easy-to-read books or magazines on the topic. Some prior knowledge will help them make their way through tougher classroom texts and promote reading comprehension. Talk about what they're reading. This "verbal processing" helps them remember and think through the themes of the book. Ask questions before, during, and after a session to encourage reading comprehension.
Drawing lots of pictures and diagrams help students' visualization and this helps them remember formulas or concept more effortlessly.
By telling them the practical application of the subject. Often students lack motivation because they think the ideas are just born and died in the pages of the book, with no real-life applications. This is where I come in and deter this misconception.
1) Use of smart technology - virtual whiteboard to lively interaction with the students 2) Call audio recording so they can access the sessions at any later time 3) Effective visualization - pictures, figures, and diagrams 4) Charts and tables 5) Problem solving - a lot!
By helping her/him derive the formulas themselves. Once they derive them on their own, they don't need any formula booklets and have got a thorough understanding of the theory. This immediately boosts their confidence.
In the first lesson - please refer to my answer above on what I'd in the first lesson.
I adjust my speed and constantly ask students if they're okay with my speed. Also, I tell them to be free to stop me at any time they want to ask questions. This puts them at ease with me and the lessons become perfectly adapted to their needs.
Books, lecture notes, past exam papers, virtual whiteboards, digital pens, and graphic tablets.
Susovan gave a comprehensive overview of the material. He was able ( by a series of questions) to detect where exactly she needs to work more and he directed her to a helpful app to practice more on specified topics. In general, the course was worth taking and eye-opening for my daughter to the nature and depth of the studying material.
Letting you know that Erika scored a 92% on her last test on binomials and probability. After your session and feedback email, she studied many hours to catch up, and it paid off. Thank you for the feedback