Caltech Ma 1 d Series: Topics, Who Takes It and Practice
A study guide for Caltech Ma 1 d Series: who takes it after the special section of Ma 1 a, what series topics it covers, and where to practice them.
Caltech Updated 3 min read
At a glance
- Course code
- Ma 1 d
- Units
- 3 units (2-0-1)
- Offered
- Second term; the 2026-27 catalog says it is not offered in 2026-2027
- Prerequisites
- The special section of Ma 1 a
- Covers
- Complex numbers, Taylor polynomials and infinite series for students who did not cover them in Ma 1 a
- Next course
- Continue with Ma 1 b and Ma 1 c
- Practice here
- Calculus 2, especially the series and power series units
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On this page
Caltech Ma 1 d is a short course on series that completes the calculus part of the core for some first-year students. It exists because Caltech offers a special section of Ma 1 a for students who need more calculus than the regular course provides. Those students spend the extra time on calculus and catch up on series in Ma 1 d. This guide explains who takes it and links each series topic to free practice.
What the catalog says about Ma 1 d
The Caltech catalog lists Ma 1 d, Series, as a 3-unit (2-0-1) course in the second term. The prerequisite is the special section of Ma 1 a. The catalog says the course is intended for students in Ma 1 a who did not have complex numbers, Taylor polynomials and infinite series during Ma 1 a, and that it may not be taken by students who passed the regular Ma 1 a.
The current 2026-27 catalog also marks Ma 1 d as not offered in 2026-2027, so check the catalog for your year before planning around it.
The catalog does not give a detailed syllabus for Ma 1 d. The topics below follow the series content of the regular Ma 1 a, which Ma 1 d replaces: Taylor polynomials and infinite series, plus complex numbers.
Ma 1 d topic map
| Series topic | Practice | Read |
|---|---|---|
| Sequences and their limits | Sequences | Limits at infinity |
| Series and partial sums | Series and partial sums | Convergence tests |
| Geometric series | Geometric series | Geometric series formula |
| The nth term test | nth term test | nth term test |
| Integral test and p-series | Integral test and p-series | Improper integrals |
| Comparison tests | Comparison tests | Convergence tests practice |
| Alternating series | Alternating series | Alternating series test |
| Ratio and root tests | Ratio and root tests | Ratio test |
| Power series | Power series and radius | Power series |
| Taylor polynomials | Taylor polynomials | Taylor series, Taylor's theorem |
Complex numbers are also part of the material Ma 1 d makes up, but they are outside the lessons on this site.
Why Caltech splits series out
Ma 1 a assumes students arrive with high school calculus. For students whose background is lighter, Caltech runs a special 12-unit section of Ma 1 a with more time on calculus itself. Something has to give, and in that section it is series. Ma 1 d fills the gap in the second term so that everyone reaches Ma 1 b and c with the same foundation.
Example problems at the Ma 1 d level
1. A geometric series.
2. A comparison. \sum_{n=1}^{\infty} \frac{1}{n^3 + n} converges because \frac{1}{n^3 + n} < \frac{1}{n^3} and \sum \frac{1}{n^3} is a convergent p-series.
3. A radius of convergence. For \sum_{n=0}^{\infty} \frac{x^n}{3^n}, the ratio test gives \left|\frac{x}{3}\right| < 1, so the radius of convergence is 3.
How to do well in Ma 1 d
- Start with geometric series. Nearly every comparison argument and every power series builds on them.
- Practice choosing tests. The choosing a test lesson trains the decision you make on every exam question.
- Keep improper integrals fresh. The integral test turns series questions into improper integrals.
- Use short daily sessions. With only three units, the course moves fast, and steady practice beats cramming.
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Geometric series
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