# 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.

Source: https://practicecalculus.com/courses/caltech-ma-1d
Updated: 2026-11-08

## 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](/learn/calculus-2), especially the series and power series units

## Key takeaways

- Ma 1 d is a short 3-unit Caltech course on series, taken in the second term.
- It is for students from the special section of Ma 1 a, who did not cover complex numbers, Taylor polynomials and infinite series in that term.
- Students who passed the regular Ma 1 a may not take it.
- The 2026-27 catalog marks Ma 1 d as not offered in 2026-2027.

**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](/courses/caltech-ma-1abc) 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](/learn/calculus-2/sequences-and-series/sequences) | [Limits at infinity](/blog/limits-at-infinity) |
| Series and partial sums | [Series and partial sums](/learn/calculus-2/sequences-and-series/series-and-partial-sums) | [Convergence tests](/blog/convergence-tests) |
| Geometric series | [Geometric series](/learn/calculus-2/sequences-and-series/geometric-series) | [Geometric series formula](/rules/geometric-series-formula) |
| The nth term test | [nth term test](/learn/calculus-2/sequences-and-series/nth-term-test) | [nth term test](/rules/nth-term-test) |
| Integral test and p-series | [Integral test and p-series](/learn/calculus-2/sequences-and-series/integral-test-and-p-series) | [Improper integrals](/blog/improper-integrals) |
| Comparison tests | [Comparison tests](/learn/calculus-2/sequences-and-series/comparison-tests) | [Convergence tests practice](/practice-problems/convergence-tests) |
| Alternating series | [Alternating series](/learn/calculus-2/sequences-and-series/alternating-series) | [Alternating series test](/rules/alternating-series-test) |
| Ratio and root tests | [Ratio and root tests](/learn/calculus-2/sequences-and-series/ratio-and-root-tests) | [Ratio test](/rules/ratio-test) |
| Power series | [Power series and radius](/learn/calculus-2/power-series-parametric-polar/power-series-and-radius) | [Power series](/blog/power-series) |
| Taylor polynomials | [Taylor polynomials](/learn/calculus-2/power-series-parametric-polar/taylor-polynomials) | [Taylor series](/blog/taylor-series), [Taylor's theorem](/theorems/taylors-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.**

$$\sum_{n=1}^{\infty} \frac{2}{5^n} = \frac{2/5}{1 - 1/5} = \frac{1}{2}$$

**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](/learn/calculus-2/sequences-and-series/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](/learn/calculus-2/improper-integrals-and-applications/infinite-limits-of-integration).
- **Use short daily sessions.** With only three units, the course moves fast, and steady practice beats cramming.

## Frequently asked questions

### What is Caltech Ma 1 d?

Ma 1 d, Series, is a 3-unit (2-0-1) second-term course for students in the special section of Ma 1 a who did not study complex numbers, Taylor polynomials and infinite series during Ma 1 a.

### Who has to take Ma 1 d?

Students who took the special section of Ma 1 a, which spends extra time on calculus. The catalog says Ma 1 d may not be taken by students who passed the regular Ma 1 a.

### Is Ma 1 d offered this year?

The 2026-27 Caltech catalog lists Ma 1 d as not offered in 2026-2027. Check the catalog for the year you plan to take it.

### What topics should I review for Ma 1 d?

Sequences and limits at infinity, geometric series, the standard convergence tests, power series and Taylor polynomials. These are the series topics the regular Ma 1 a covers.

### How many units is Ma 1 d?

Three units, listed as 2-0-1: two hours of class, no lab and one hour of outside preparation per week.