Skip to main content

Awesome things to know

My Harvard-MIT Mathematics Tournament Experience

The Harvard-MIT Mathematics Tournament (HMMT) is a high school competition that is held in Cambridge, MA and the competition location typically alternates between Harvard University in November and MIT in February. This tournament attracts many top students in mathematics from everywhere. Like PUMaC, HMMT is also organized by student volunteers who are currently attending Harvard and MIT.

I never participated in the November contest but got a chance to participate in the February one. The differences between the two are listed here. November one can have 6 students and the February one can have 8 students in one team. I have to admit that this is not an easy contest and so guidelines of knowing your level and participating in the right one is important. For example, if you can do first few problems of AIME comfortably, then participate in the November one where as if you can do later AIME problems and AMO problems, then participate in the February one.

Overall, I was exhausted at the end of the day after doing many hours of math. We started in the morning with the Team (Proof based) round first then you get 3 individual tests for Algebra, Geometry, and Combinatorics which are 50 minutes each. These problems are like harder AIME problems and I was able to solve four in each category. We got a nice lunch break after the individual round and then proceeded to the Guts round. This is a fun round where you can see how your team is doing on a big screen in the MIT Math building. At one point, my team was in the top 15 teams which made me feel very proud. The best way to prepare for this contest is to practice using previous tests which are here. I also really enjoyed practicing with my team a few weeks prior to the test. We met for a few days on the weekends.

Overall, the student volunteers at Harvard and MIT did a wonderful job in organizing the event with close to 1000 high school students on the campus. I also got a chance to visit MIT and sit through their information session.



“Math departments fail too many calculus students….

David Bressoud is a well-known mathematician who is a Professor of Mathematics at Macalester College and a former President of the Mathematical Association of America (MAA).  In this article, he advocates for colleges changing the way they teach calculus. He argues that the current model of instructor-led teaching is outdated and that even the students who pass the introductory courses in calculus are not always prepared for the higher level ones. Dr. Bressoud recommends active engagement in mathematics, which is usually referred to as “active learning.”

NSF funded a $3 million five-year project called SEMINAL, which stands for Student Engagement in Mathematics Through an Institutional Network for Active Learning. 12 public universities are working together on this project to show how active learning can be used in mathematics classes from precalculus through higher forms of calculus.

Even in 2018, I feel that calculus and related courses are seen as tough and gatekeepers for many aspiring students, whether they want to pursue STEM related education or economics and finance. In my high school, performance in calculus courses is critical to advance to the next level and to qualify for honors level courses in subjects like Physics or Computer Science. Even the Wharton @ Penn undergraduate admissions list shows the requirement to “have taken calculus during high school.”

I am fully in agreement with this article, in that we need to revamp how calculus is taught in high schools and colleges. Calculus is not seen as a very inclusive class which discourages many girls and minorities to enroll, with media as well stereotyping calculus students in a negative way. This research report from Dr. Bressoud and others does a nice job of giving a lot of details including this profound statement: “The worst preparation a student heading toward a career in science or engineering could receive is one that rushes toward accumulation of problem-solving abilities in calculus while short-changing the broader preparation needed for success beyond calculus.”


Math Majors Gender Distribution

“Do girls who participate in math competitions through high school typically major in STEM fields when in college?” I get asked this question many times. I have done a few surveys on this topic and will share the results in the next few weeks.

I wanted to share the analysis done by the National Student Clearinghouse® Research Center™. The Research Center works across many higher education institutions and educational organizations to inform practitioners and policymakers about student educational pathways as per their website.

The following charts shared in the report basically outline that the number of girls who pursue Bachelor’s degrees in mathematics have declined from 2004 through 2014. The Master’s and Doctorate numbers have remained constant and continue to be discouraging.

WP-Snapshot-012715-5-900x625 WP-Snapshot-012715-4-900x625 WP-Snapshot-012715-3-900x625

Women are approximately 15% of tenure faculty positions (makes sense based on the Doctoral data above) in mathematical sciences research universities in the United States. Dr. Sen and Dr. Topaz found out that 8.9% of the 13067 editorships in mathematical sciences (435 journals) were held by women. The research concluded that the degree of underrepresentation of women on mathematical sciences journal editorial boards is far more severe than in the mathematics field overall.

I personally believe that all of these data points are related and attrition of girls continue to be higher at the higher levels in the field. We as a society and community need to continue to encourage girls at each and every stage (master’s; doctorate, faculty, tenure track and so on…) to break this trend.


My PUMaC experience

The Princeton University Mathematics Competition (PUMaC) is a student-run competition organized by the Princeton University Math Club since 2006 in Princeton, NJ.  2017 competition was held on Princeton campus on November 18th. You can find all the previous years’ problems and solutions here which can be very helpful to prepare for this competition. I would highly recommend to read the FAQs before participating in this competition.

I found PUMaC to be very intense and challenging competition. One week before the competition, you get Power Round questions. Power Round is a tough and time consuming round. You get the opportunity to work with your team for a week on these problems. You submit the power round before the competition begins on the campus. You will take individual tests in two sections of your choice (algebra, number theory, combinatorics, geometry), then compete in a team round, a live Round, and if you qualify then the Individual Finals. Princeton student volunteers had fully organized this contest and I found them nice, warm, and welcoming whenever we had questions or clarifications. Besides fun math activities and delicious lunch, there was also a session about majoring in math at Princeton with Prof. Mark McConnell which was super helpful.

I really enjoyed being part of a competition team and I met most of my team members for the first time on the day before the competition. This competition challenges you individually and as a team which I found a great learning experience.


USA Mathematical Olympiad – Gender Distribution

The United States of America Mathematical Olympiad (USAMO) is an invitation only high school mathematics olympiad that is held annually in the United States. USA(J)MO serves as the final round of the AMC 10/12 contests. USAJMO was introduced to qualify students based on their scores in AMC 10+AIME exams where as USAMO qualification is based on AMC12+AIME exam scores.

MAA (Mathematical Association of America) was kind enough to provide me with various statistics of USA(J)MOs for the past five years. Unfortunately, given the drastic drop in number of female students who qualify for the AIME, the trend of female qualifications in USA(J)MO is equally discouraging. As you see below, the qualification of girls have stayed mostly constant over the past five years. Each year nearly 500 students qualify for USA(J)MO and the average number of girls who qualify has stayed constant ~10%.


I also found it interesting that the average scored of males vs females were not that different, however, most of the high scoring students in USA(J)MO are males. MAA now invites a few girls based on their scores in USA(J)MO to Mathematical Olympiad Summer Program (MOSP) who are then further trained for European Girls Mathematical Olympiad.


Emergence of Gender Stereotypes and its impact on girls’ interests

I’ve always been a huge fan of the profound research done by Dr. Leslie and Dr. Cimpian on gender stereotypes.  Their study on how misplaced importance on brilliance in a field sometimes discourages the minority in that field (women and African-Americans) is a fascinating one. In their latest study, they surveyed 2,000 professionals in 30 academic fields. The purpose of the survey was to determine how strongly the respondents believed that signs of brilliance, as measured by field-specific ability belief index, resulted in doctorate degrees being awarded in their discipline. It makes a lot of sense that fields with a higher index such as computer science, math, engineering, chemistry and philosophy, awarded relatively fewer advanced degrees to women and African-Americans whereas Art History, Psychology, Literature and other humanities disciplines awarded many more advanced degrees to women and minorities. I especially liked the critical observation related to the comparison between a fixed and growth mindset made in this study. The obsession in STEM fields with being brilliant or genius and the reinforcement of that in society, schools, media and others deter the very same people who we want to encourage to participate more. I see this phenomena occur often in the case of math competitions in middle school and high school, where unfortunately hard work and a growth mindset are not encouraged at all, and the society continually wants to reinforce the concepts of brilliance. For example, when girls do well in math, then “it must be because of their hard work” whereas boys when they do well then “it must be because they are brilliant”. This creates a vicious cycle that causes girls to shy away from participating in problem solving-based math competitions, which could benefit them a lot and eventually help them pursue advanced degrees in STEM including Ph.D.s.

Dr. Leslie and Dr. Cimpian were also featured on primetime television where they disclosed findings from their new study.

This study offered insights that girls at the age of 6 are less likely than boys to believe that they are really smart. Girls then start to avoid activities that they believe require them to be really smart. In Silicon Valley and a few other industries, there are a lot of efforts to encourage hiring of more women in STEM-related disciplines. However, if we do not address the issues outlined in the study where gender stereotypes are formed early in girls, most of the diversity-related initiatives will have mediocre success at best.


She will always be an inspiration…..

“But most of the time, doing mathematics for me is like being on a long hike with no trail and no end in sight.”

“I got involved in Math Olympiads that made me think about harder problems.”

-Dr. Maryam Mirzakhani (2014)

The world lost Dr. Maryam Mirzakhani on July 14th. She was so young and despite her profound achievements to date, she was on a path to contribute significantly more to the fascinating field of mathematics.

I firmly believe that there are many girls and women all over the world, like myself, who feel a deep sense of loss over Dr. Mirzakhani’s death. She was such an inspiration to so many girls who loved math and were looking for a female role model. Dr. Mirzakhani achieved so much at such a young age and defied all the odds on her journey to success.

Dr. Mirzakhani got internationally recognized when she became the first woman to win the Fields Medal in 2014 (which is awarded every four years), a top prize in mathematics. The Fields Medal, also known as the Nobel Prize of Mathematics, was awarded to her at the International Congress of Mathematicians in Seoul, South Korea. This was unprecedented, as the 52 previous recipients had all been men. When I first read about it in 2014, I couldn’t believe it.

Dr. Mirzakhani always credited inspiring teachers and supportive friends during her high school, and college years.  Her middle school teacher discouraged her interests since she wasn’t at the top of her class. But it all changed when she attended an all-girls high school. Dr. Mirzakhani credits her principal who encouraged and permitted her to compete for Iran’s International Mathematical Olympiad, even though she was the first girl to do so. Dr. Mirzakhani entered in many mathematical competitions, eventually represented Iran at the International Mathematical Olympiad, and won gold medals in 1994 and 1995, while scoring a perfect score in 1995. She earned her bachelor’s degree at Sharif University in Tehran and then went to Harvard, where she studied under the direction of Curtis McMullen, also a Fields medallist.

This interview gives a lot of insight into Dr. Mirzakhani’s personality, ambition, character, and her journey.

Dr. Mirzakhani joined the faculty of Stanford University in 2009 from Princeton, where she served as a professor in the Department of Mathematics until her death.

I sincerely hope that we do not have to wait for another 52 male recipients before another woman wins the Fields medal. Dr. Mirzakhani’s journey, achievements, persistence, and patience will always be an inspiration for many girls, teachers, and women for decades to come.

Dr. Boaler at Stanford has written a heartfelt note that I highly recommend to read.


Gender Imbalance in IITs (Indian Institute of Technology)

IITs are considered prestigious institutions in India with very low acceptance rates and have history of producing top technical minds similar to MIT in USA.  Even Fortune magazine covered the network and brand of IIT in this article in year 2000 at peak of the dot com boom.

The gender ratio in IITs continue to be imbalanced as per this article with specific data. Out of approximately 10000 students who get admitted every year based on their scores in Joint Entrance Examinations, only 10% of admitted students are girls from 2011-2015. JEE covers questions from Mathematics, Physics, and Chemistry. I have discussed the pattern of girls achieving high scores in AMCs and AIMEs in the past. The similar is true here that the number of girls at top end of the scores in JEE tend to be fewer and there are potentially a variety of reasons for that including cultural reasons where Indian parents don’t tend to send their daughters to expensive coaching camps away from home.

Here is the good news. IITs have decided to admit more women beginning 2018 to buck the trend. The goal of these additional seats just for girls is to get the percentage of females to 20 over the next few years. This is encouraging as there are many cultural and socioeconomic reasons on why the female percentages were so low to begin with. IITs also made a smart decision and decided to add additional seats for girls rather than making it a zero sum game within existing seats. Also, girls have to still score high in the JEEs to get accepted which means the bar of acceptance has not been compromised.





My maiden experience with USA(J)MO

The United States of America Mathematical Olympiad (USAMO) is a proof based competition that is held annually in the United States. This competition has served as the final round of the AMC series of contests and the scores are used to determine further qualifications leading up to selection of USA team for the International Math Olympiad.

First, the qualification scores for USAMO were very high this time (relatively) and were split based on A and B exams as well as two AIME exams. Only 500 students qualified across the country for USAMO and USAJMO. The scores imply that one has to score high both on AMCs (120-130) and AIME (10+) to qualify for USA(J)MO exams. It is tough to determine how many girls qualified as gender data is not available, however, historically the number has been 7-10% of the total qualifiers.

AIME I based Qualifications

  • USAMO cutoff: 225(AMC 12A), 235(AMC 12B)
  • USAJMO cutoff: 224.5(AMC 10A), 233(AMC 10B)

AIME II based Qualifications

  • USAMO cutoff: 221(AMC 12A), 230.5(AMC 12B)
  • USAJMO cutoff: 219(AMC 10A), 225(AMC 10B)

This exam was intense for me. It is a  two day, 9 hours exam (split in two individual 4.5 hour sessions) that is organized at a particular time across the country which means you end up missing most of your school classes. You get 3 questions each day and it took me more than two hours to solve the first problem on Day 1 and 3 hours to solve 5th problem on the second day. I had very little experience preparing for such an exam but have heard that taking courses offered by AoPS definitely help out.

Each problem is worth 6 points and maximum score is 42. The average for JMO was 13.3 and for AMO was 11.8 with some students scoring zero.

There are many different ways to prepare for this test. This is a good link for more information. Overall, it was a great experience for me to do proofs which is helpful for some other college math competitions as well.


Math Day for Middle School Girls at Stanford

I was fortunate enough to witness “Math Day for Middle School Girls,” a workshop for girls that was hosted by Youcubed, a nonprofit center which is part of Stanford’s Graduate School of Education. Youcubed’s mission as per their website— “Our main goal is to inspire, educate and empower teachers of mathematics, transforming the latest research on math learning into accessible and practical forms.”

Youcubed was founded by Dr. Jo Boaler with Department of Education at Stanford, who has done a lot of research on mathematical mindset and published many books related to that topic.


About 120 girls from local middle schools participated doing fun math activities throughout the day. There were many inspirational speeches by faculty, undergraduate students, and  Dr. Persis Drell who is currently Stanford Provost. Girls who participated definitely enjoyed the day in a fun, non-competitive environment while learning the importance of Math.

More details can be found here.