How to learn English Vocabulary efficiently


As some of you know, I am now the Founder & CEO of TrueShelf Inc, an EdTech startup based in the Bay Area. TrueShelf is aimed at developing platform, content and products to aid intuitive, visual, social, adaptive and personalized learning. TrueShelf consists of two main components: TrueShelf Online Network and TrueShelf Apps. Read our FAQ for more details.

Today’s post is about TrueShelf apps, intuitive and visual learning apps that are carefully designed to help students learn specific concepts in a systematic and adaptive manner.

Recently we released our True Vocabulary app, our first adaptive learning app. The existing solutions to learn english vocabulary are either too hard-to-use and/or expensive and/or old-fashioned (e.g. flashcards). Our app is focused primarily on automatic personalization and ease-of-use. It has already received more than 25,000 downloads on the iOS app store. If you are preparing for GRE, SAT, GMAT, ACT, CAT or simply interested in improving your english vocabulary, True Vocabulary app provides an efficient and elegant step by step adaptive learning process. It is an intelligent personalized vocabulary tutor.

True Vocabulary uses an intelligent algorithm (based on the concepts of spaced repetition, Leitner system and lexical cohesion) to design adaptive multiple-choice vocabulary quizzes. Learning tasks are divided into small sets of multiple-choice quizzes designed to help you master the basic words before moving on to the advanced words. Words closely related to your hardest words are selected more frequently in the quizzes. For a fixed word, the correct and wrong answers are selected adaptively giving rise to hundreds of combinations. After each wrong answer, you receive a detailed feedback with the meaning and usage of the corresponding word. Coins, Gems and Levels are unlocked adaptively to motivate, evaluate and reward the learner.

Download our True Vocabulary App and let me know your feedback (or) suggest new features.


This is just the beginning of our journey to make education elegant, efficient and painless for hundreds of thousands of students and teachers. In future posts, I will talk more about TrueShelf’s vision and roadmap. Stay tuned.

Happy New Year

Happy New Year to everybody. I am starting to a new blog on medium to discuss my entrepreneurial experiences and life. Check out my latest blog post titled ‘Happy New Year‘ discussing my life in 2015 and predictions for 2016. I will continue using this wordpress blog to post math-related posts. Follow me on twitter ( @kintali ) to get updates on my new blog posts on medium.

Forbidden Directed Minors and Directed Pathwidth

Today’s post is about the following paper, a joint work with Qiuyi Zhang, one of my advisees. Qiuyi Zhang is now a graduate student in the Mathematics department of Berkeley.

  • Shiva Kintali, Qiuyi Zhang. Forbidden Directed Minors and Directed Pathwidth. (Preprint is available on my publications page)

Undirected graphs of pathwidth at most one are characterized by two forbidden minors i.e., (i) K_3 the complete graph on three vertices and (ii) S_{2,2,2} the spider graph with three legs of length two each (see the following figure).


Directed pathwidth is a natural generalization of pathwidth to digraphs. We proved that digraphs of directed pathwidth at most one are characterized by a finite number of forbidden directed minors. In particular, we proved that the number of vertices in any forbidden directed minor is at most 8*160000+7. Ahem !!

This paper falls in the “directed minors” part of my research interests. In an earlier theorem, proved in April 2013 (see this earlier post), we proved that partial 1-DAGs are characterized by three forbidden directed minors. In a similar vein, I conjectured that the digraphs with directed pathwidth at most 1 are characterized by a finite number of forbidden directed minors. I assumed that the number of forbidden directed minors is number is around 100. So we started this project in May 2013 and started making a list of carefully constructed forbidden directed minors and tried to extend our techniques from partial 1-DAGs. Here is an initial list of minors we found.


All the forbidden minors we found, looked very cute and we assumed that a proof is nigh. Soon, we realized that the list is  growing quickly and none of our earlier techniques are applicable. After almost an year of patient efforts and roller coaster rides, we proved our finiteness theorem in May 2014, two weeks before Qiuyi Zhang’s thesis defense. It took us 10 more months to get the paper to its current status. So this is a two year long adventure.

I am hoping to prove more theorems in the “directed minors” area in the coming years. The current paper taught me that patience and focus are big factors to make consistent progress. There should be a nice balance between `proving new theorems’ and `writing up the existing results’.