Letter to the editor: A response to the Editorial Board about MATH 51

June 11, 2018, 9:24 a.m.

We read with interest the June 6 editorial concerning your perception of large introductory courses here, in particular of Math 51, which provided the title for the editorial. We wish the Editorial Board had contacted the Math department, as well as other departments mentioned, to get a broader perspective. We regret that the editorial may not contain the most accurate information about Math 51, for example, and we would like to highlight some salient facts.

Though Math 51 has several hundred students enrolled each quarter, it should not be regarded as a large lecture class. Thanks to a generous program sponsored for many years by VPUE,  Math 51 lectures have around 50 students each; this allows for closer interaction between students and the instructor. While the editorial does not make it clear, our department always eschews the use of PowerPoint slides, for exactly the reasons you noted: it is far too easy to advance quickly through slides, whereas a traditional blackboard lecture allows for a more personal and human interaction and pace.

We recognize that not every instructor has an equally polished style, and we provide oversight and training for all new instructors to make improvements. While it is a common truism that professors at Stanford are here to do research and some may be less interested in teaching, the Math department is highly conscious of the importance of good teaching. We take very seriously our role in providing instruction on material that is essential knowledge in many fields. The teaching record of everyone appointed to a faculty position in our (and every other) department is scrupulously examined.

There is no doubt that every course needs regular review and updating, and Math 51 is no exception. Indeed, the course has evolved steadily through the 20 years since it was created.  In the past few years, we have incorporated features of what is commonly called “active learning,” following advice and recommendations of top experts in education research, from our GSE and elsewhere.

In the coming academic year there will be an even more significant change. A new textbook will be rolled out starting Fall 2018, developed by a team of Math faculty over a four-year period, in consultation with colleagues from many other departments at Stanford. The new textbook will be freely available to students, and is specifically adapted to this course. We believe that this book will make the course more accessible, and more useful for Stanford students as they pursue majors in departments across all scientific and engineering fields.

This new textbook involves not only a significant reorganization of the curriculum, but also an emphasis on contemporary applications of fundamental topics such as optimization and the parts of linear algebra that are important for data science, machine learning, economics and many subjects in the social and natural sciences.  This effort has also involved evaluating the design of homework, pre-reading and exams to find the right balance so that students can most effectively learn this material amidst their busy academic schedules.

We are well aware that mathematics is a challenging subject to learn, and we make every effort to provide services for students in the form of numerous office hours and after-hours tutoring.  We would be very happy if these services were better utilized, and are always grateful for suggestions of other ways we can help students master the material. Decades of educational research have shown that nothing can replace time that a student spends thinking about the material, reading the text or other sources, and working on problems alone or in groups.

While Carta may be useful in some ways, we urge students to take what they see there with a grain of salt. Reviews and grade information there are often obsolete, and just as you would with any product review or news, consider potential biases of who wrote it. We regret that the editorial propagates the myth that Math 51 during the Winter has “a more forgiving curve,” which is completely false. Moreover, the design of Carta makes it impossible for instructors or other faculty to see comments there, so such feedback is not available to the academic departments.

We are proud of Math 51 for many reasons. This course was one of the first, perhaps the first, at this level in the country to completely integrate multivariable calculus with linear algebra. The recent explosion in data analysis has made linear algebra an ever more essential subject for every budding engineer and scientist to master. The depth in which linear algebra is treated in Math 51 makes it the wisest choice for students to help them to operate at the highest level, whatever their later field of study may be. For example, CS229 on Machine Learning and CS230 on Deep Learning specifically recommend courses resting on Math 51 for the linear algebra background.

We welcome feedback about Math 51, and indeed any of our courses, and are always looking for ways to improve what we do and make our courses more useful for Stanford students.


Prof. Ralph Cohen, Prof. Brian Conrad (Math DUS), Prof. Eleny Ionel (Math Dept. Chair), Prof. Rafe Mazzeo, Prof. Andras Vasy, Prof. Akshay Venkatesh, Prof. Brian White

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