Cohort One AY: 2020 - 2021
All done with an interview.
Cohort Two AY: 2022 - 2023
Basic math + English writing tests & an interview
Cohort Three AY: 2024 - 2025
Basic math + English writing tests & an interview
Basic math - Calculus - Linear algebra - English test - Interview questionnaire (following section)
Cohort Four AY: 2026 onward (apply any time)
Complete this admission form, and expect to hear from us within one month.
Interview Questionnaire
Questions included in the interview ranged from ideological self-identification to real analysis, abstract algebra, and linear algebra
Ideological Self-identification
What is special about you compared to other candidates?
In MAC, we have many reading courses and projects plus extra homework and presentations. How are you supposed to manage yourself?
Injection, surjection, bijection
What does a function mean?
One should clearly distinguish the difference between function and map.
What is an injective/ surjective function?
Give one injective function but not surjective, surjective but not injective, both injective and surjective, and neither injective nor surjective.
What does a bijective function mean in a category of sets?
Those two sets are mathematically equivalent/ same. The two-sided composition of functions produces a bijective function, not one-side doing. It is because f: X -> Y, g: Y -> X, gf: id_X, we get f is surjective & fg: id_Y, we have f is injective.
Can you define the concept of sameness in the category of groups/ vector spaces/ topological spaces? How?
Limit, derivative, integration
What does a limit/ derivative/ integral of a function mean? including the definition and criteria to make it well-defined.
Give one example where we cannot do limit/ derivative/ integral.
Can we do a limit/ derivative/ integral in the category of groups/ vector spaces/ topological spaces? How?
Properties of sets
What is a limit/ interior/ exterior/ boundary/ accumulation point?
What is an open/ closed set?
Give one open set, closed, both open and closed, neither open nor closed.
Why do we need to define the concept of topological spaces in terms of open/ closed sets?
Miscellaneous questions (may/ may not be asked if time is not permitted)
What does a plane/ space/ dimension/ distance mean in mathematical language?
How do we do addition and multiplication on matrices? But why do we need to do so?
What are the differences between the first and the second derivative or any higher derivative?
*If you cannot answer one of these questions, please tell us anything you know about mathematics.
