How to Apply to Mathematics at Caltech: Admitted to the Institute First, Everyone Takes the Same Core in the First Year and Chooses an Option at Its End, with Requirements for Domestic, International (Including Chinese) and Transfer Students

The California Institute of Technology (Caltech) is in Pasadena, California. The website calls majors “options.” The Institute has six academic divisions, one of them Physics, Mathematics & Astronomy; the catalog lists the Mathematics option under the mathematics department, and the pages read do not say explicitly which division it belongs to. The catalog places Applied and Computational Mathematics (ACM) in the Computing & Mathematical Sciences department. Below is what Caltech’s website says, for domestic students, international students (with a separate section for applicants from China) and transfer students. Computer science, economics, engineering and other majors are not covered here; the site has separate articles.

1. The mathematics options

• Options: the options most directly about mathematics are Mathematics and Applied and Computational Mathematics (ACM). Information and Data Sciences is also listed but is not covered here. The catalog’s transfer section refers to a Caltech Bachelor of Science degree; the pages read do not separate a B.A., or a pure, applied or statistics track.
• Mathematics option (catalog): gives students an understanding of the broad outlines of modern mathematics, introduces current research and prepares them for advanced work in pure mathematics or related fields. Students study the structures of algebra, analysis and geometry and the rudiments of combinatorics and set theory, learn to write complete proofs and use computational tools. The schedule is flexible.
• Required courses (catalog 2026-27): Ma 2, Ma 3 (or Ma/ACM/IDS 140 a), Ph 2 bc or Ph 12 bc, Ma 5 abc (abstract algebra), Ma 10 (oral presentation), Ma 108 abc (classical analysis), Ma 109 abc (geometry and topology), discrete mathematics or related courses, and 45 more units of advanced math (Ma 110 to 190 or ACM 95 and above). Passing grades are needed in a total of 486 units, including the core.
• ACM option: the catalog says it combines basic studies in mathematics with considerable involvement in applications such as fluid mechanics, materials science, mathematical biology, engineering applications, image processing and mathematical finance. Requirements include Ma 2, Ma 3, Ma 108 ab, CS 1, ACM 11, ACM 95 ab and ACM/EE 106 ab, with a C- or higher. Students who want to pursue a second option simultaneously must meet all ACM requirements and talk with the option representative; the catalog says approval is “contingent on good academic performance… and demonstrated ability for handling the heavier course load.”
• Minor: there is also a mathematics minor: Ma 2, Ma 3 or equivalent, two three-term courses among Ma 5abc, Ma 108abc and Ma 109abc, and 18 more units of math courses.
• Research areas: the catalog lists the faculty’s areas: algebra, algebraic geometry, analysis, combinatorics, geometry and topology, mathematical logic, mathematical physics, noncommutative geometry and number theory. The admissions site says nine out of ten students do research while at Caltech, whatever their major.

2. How admission works: the Institute first, an option at the end of the first year

• You do not apply to an option: the website says you do not declare a major until the end of your first year, and every first-year student takes the same classes in the first two terms. The supplemental essays have a required question asking which one or two areas of interest you would choose today (150 to 200 words), and Caltech says you are under no obligation to follow that choice.
• Quotas by option: the pages read do not mention limits for the Mathematics option or any other; this is not published, so ask admissions.
• Declaring an option and changing into mathematics: the pages read do not describe the declaration procedure or any grade conditions, nor the conditions for moving into mathematics; this is not published, so check the catalog or ask the academic offices. The catalog does state one related rule: a student whose grade-point average in mathematics and ACM subjects is below 1.9 at the end of the academic year may be refused permission to continue in the mathematics options.
• First-year math advice: the catalog says first-year students considering a mathematics major should know the department strongly recommends the analytical track of Ma 1 bc.

3. Preparation

• High school courses: four years of math including a year of calculus, a year of physics, a year of chemistry, biology recommended; four years of English; two years of history or social sciences (three or more recommended). The site says students who run out of math before senior year need not have four years, but Caltech expects them to have taken as much math as possible, including a year of calculus.
• If calculus, chemistry or physics was not available: the applicant and counselor must document the unresolvable issue, and then the requirement can be met with exam scores or a Schoolhouse.world course challenge: a 5 on AP Calculus AB or BC, Chemistry, Physics 1, 2 or C; a 6 or 7 on IB Mathematics HL, Chemistry or Physics (SL or HL; the catalog says IB Mathematics SL does not meet the requirement); or Schoolhouse.world’s AP/College Calculus BC, Chemistry or Physics 1 challenges. AP and IB exams must be taken by the deadline, and Schoolhouse proof is due within a week after it. The admissions page states these rules for fall 2026 applicants, so check whether they are the same for fall 2027. The catalog lists Schoolhouse’s calculus as “AP/College Calculus AB or BC” where the admissions page says BC, a small difference.
• First-year math: everyone takes Ma 1 abc (calculus of one and several variables, and linear algebra) in the core. Before the first year, all new students take the Foundations Assessment (high school chemistry, physics and math), which decides placement in Ma 1 a; those who want to place out of part of the core math can take an advanced placement exam over the summer. The catalog says AP or IB credit is not automatic; credit or placement is decided by the department faculty and awarded at fall registration. The pages read have no course-by-course AP/IB credit table; this is not published, so ask the department.
• Other curricula: IB requires Higher Level Math, and GCE A-Level requires A-Level Maths (international applicant page).
• Math competitions: the pages read do not say how competitions are viewed; this is not published.

4. Rounds, materials and testing (fall 2027)

• Two rounds: Restrictive Early Action (REA, non-binding but you may not apply early action or early decision elsewhere, with exceptions) closes November 1, 2026 with materials by November 6 and decisions in mid-December; Regular Decision closes January 4, 2027 with materials by January 10 and decisions in mid-March; the reply date is May 1, 2027. QuestBridge is a separate route. Caltech says admit rates in the two rounds differ negligibly and tells applicants not to apply REA just to improve their chances. One paragraph on the deadlines page gives the Regular Decision reply date as “May 1, 2026,” which looks like a typo; other pages say 2027.
• Application and fee: the Common App or QuestBridge application; USD 85 fee, with fee waivers available.
• Essays: Caltech’s own questions are updated each summer. The 2026-27 set has a required STEM interest question, one short “scholarly character” essay (a choice of two prompts, 200 words), two “scientific drive” essays (choose two of three, 200 words each), a “fun question” (100 to 150 words) and an optional academic-context question. The site says faculty read them, so you can get technical.
• Recommendations: two teacher letters plus a school report. One letter is from a STEM teacher (the admissions page lists calculus or beyond, chemistry, physics or biology; the catalog lists math, chemistry, physics or biology) and one from a humanities or social science teacher. The international page lists STEM as math (calculus or beyond preferred), physics, chemistry or biology. A math teacher is one of the accepted choices but not the only one.
• Testing: the SAT or ACT is required, with no minimum score and superscoring. Caltech uses a “bucket” system: an SAT section score of 780 to 800 or 750 to 770 is shown to the committee only as a bucket, while scores below 750 are shown exactly. All AP and IB exams taken must be reported, whatever the score.
• Supplemental materials: a research paper or publication, or a STEM or non-STEM portfolio, submitted through the applicant portal after the deadline.

5. Domestic students

• Cost: for 2026-27, on-campus undergraduates: tuition USD 68,574, fees 2,655, housing 12,711 and meals 9,285, for direct costs of 93,225; books and materials 1,428 and personal expenses 3,969, for indirect costs of 5,397. The student health plan is extra at USD 5,388 (optional with comparable coverage), and new students pay a one-time USD 600 orientation fee. The costs page gives one set of figures, with no in-state and out-of-state split and no resident preference or guarantee mentioned; this is not published.
• Aid: Caltech says it meets 100% of demonstrated need and is need-blind for domestic students (including undocumented and DACA students). Aid is need-based only; Caltech awards no merit scholarships. The site says most students from families earning under USD 100,000 (with typical assets) can expect a no-loan package covering tuition, fees, housing and food, and most under USD 200,000 can expect tuition to be covered. For the class entering in fall 2026 the average grant was just under USD 69,000.
• Department scholarships and research: the pages read do not mention scholarships specific to the mathematics department; this is not published. The site says nine out of ten students do research, and a summer research term is available.

6. International students

• Definition and review: an international applicant is neither a US citizen nor a permanent resident and attended secondary school outside the US. Apart from financial need, application and review are the same as for other applicants. All materials must be in English; non-English documents need the original and a translation, and an application with any untranslated part will not be reviewed.
• English: required unless English is your native language or the main language of instruction at your school: IELTS 7 overall and in each area; TOEFL taken before January 21, 2026: 100 with 25 in each area; on or after January 21, 2026: 5 with 5 in each area; Duolingo 130 overall and in each area. The exam must be taken before the deadline. If English is the main language of instruction but not your native language, a score is strongly recommended. InitialView, a recorded conversation and writing sample, is recommended but not required and does not replace the exam.
• Financial aid: apply for aid at the time you apply for admission and confirm the International Financial Aid Statement of Intent. The site says that if you do not apply for or receive aid for the first year, you may not apply later (citizens of Canada and Mexico may be exceptions). Caltech is need-aware for international applicants because aid is limited, and also says it meets the full demonstrated need of admitted students, covering tuition, housing, dining, books, fees and personal expenses.
• Curricula: IB students need Higher Level Math; A-Level students need A-Level Maths; students in India must complete both year X and XII state board or CBSE examinations. Students taking STEM classes only in the last two years need two English and two social studies classes in the first two years.
• Transcripts: official transcripts sent directly by your school with course titles, grades and predicted grades; there is no need to convert to the US system.

7. Applicants from China

• Gaokao: the pages read do not say how Gaokao results are used; this is not published, so ask admissions using the contact on the website.
• Transcripts and verification: follow the international rules above: official transcripts sent by your school, with predicted grades, and English translations. The pages read list no China-specific exam certificates, credential agencies or interviews; confirm with admissions.
• Curriculum: the math, physics and chemistry requirements above apply. The website explains IB and A-Level equivalents but does not map the Chinese high school curriculum; this is not published.
• English and aid: the international English scores and need-aware aid rules above apply.

8. Transfer students

• Eligibility: you must have finished secondary school and earned credit at a college or university. Caltech admits transfers for fall only, into the sophomore or junior class (the catalog says not the senior year); students who already hold a bachelor’s degree are not eligible.
• Dates: the transfer pages list a February 1, 2027 deadline, entrance exams due February 15, a mid-April decision and a June 1 reply date, but also say that the fall 2027 application and requirements will be available in late fall and that the requirements shown are for fall 2026 applicants, so verify the dates for fall 2027 entry. The catalog gives the same February 1 date but says decisions come in early May, which differs from the admissions page’s mid-April.
• Materials: USD 85 fee; math and physics entrance examinations (4 hours each, taken at home on your honor, with no references or calculators); two letters from college faculty in math, science or engineering; official transcripts from all colleges and your secondary school. SAT and ACT scores are not required and are not reviewed. The exams are based on single and multivariable calculus, linear algebra, classical mechanics, electromagnetism and statistical physics, and special relativity.
• Credit: credit and class standing are decided after admission; Caltech gives a preliminary estimate, but registrar and faculty review each course individually, so it cannot answer whether specific coursework will be accepted beforehand. Transfer students spend at least six terms at Caltech and earn at least 216 units there, not counting math and science core courses. They may choose any undergraduate option and must satisfy that option’s requirements.
• International transfers: English scores IELTS 7, TOEFL 100 (25 in each area) or Duolingo 130; financial aid is not available to international transfer students, who must expect to cover the full cost.
• 3/2 plan: with 13 partner liberal arts colleges listed on the site (for example Pomona, Reed and Wesleyan), due April 1; applicants need at least a year of calculus-based physics and mathematics (including multivariable calculus and differential equations) and a year of chemistry.

Checklist

Domestic students:

• Four years of math (with calculus), physics and chemistry in high school; apply by November 1 (REA) or January 4 (Regular Decision) and submit the SAT or ACT
• Two teacher letters (one STEM, one humanities or social science); write the Caltech-specific essays
• Take the Foundations Assessment the summer before; choose Mathematics or ACM at the end of the first year

International students (including those from China):

• IELTS 7, new-scale TOEFL 5 or Duolingo 130 if English is not the language of instruction; translate all documents into English
• Apply for financial aid with the admission application; it cannot be added later
• Ask admissions whether Gaokao results can be used

Transfer students:

• Complete calculus, linear algebra, mechanics and electromagnetism; prepare for the February 1 application and February 15 exams; verify the dates for fall 2027

Sources: Caltech, Majors and minors; The first year; Academic requirements; First-year application requirements; Deadlines; Standardized tests; Supplemental essays; International applicants; Transfer deadlines; Transfer requirements; Transfer entrance exams; International transfer applicants; Afford; Costs; Catalog: Mathematics option; Catalog: ACM option; Catalog: mathematics research areas; Catalog: first-year admission; Catalog: transfer admission; Catalog: core requirements. Dates are for fall 2027 entry and costs are for 2026-27. Check Caltech’s website for the latest.