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Calculus theorems need hypotheses
Real analysis is where results that once felt automatic start to depend on exact assumptions such as compactness, continuity, or differentiability.
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01:640:311 · Mathematics · School 01 — New Brunswick School of Arts and Sciences
Introduction to Real Analysis I is Rutgers Math's first standard analysis course after Math 300. Official department pages describe it as an introduction to the language and core concepts of analysis, centered on the real numbers, sequences, limits, continuity, and differentiation in one variable, while also emphasizing understanding definitions, following proofs, testing conjectures, and communicating mathematics clearly.
Can I take it?
Differential Equations For Engineering And Physics · Intro Math Reasoning · Elementary Differential Equations
How hard?
Students rate teaching
SIRS · 861 responses · 2014–2025
Spring 2027
3 open in snapshot
When it meets
Livingston
AI-generated overview
Higher means more demanding · AI summary
5 units · topic sequence may vary by instructor
The course opens by reframing familiar calculus objects in a more rigorous style. Students are expected to read definitions closely, distinguish examples from proofs, and work carefully with the structure of the real numbers.
Sequences are often the first major proving arena in the class. Rutgers topic lists consistently place convergence, monotone sequences, and Cauchy-style reasoning near the center because they train the epsilon-level discipline used throughout analysis.
After sequences, the course usually revisits core calculus ideas from first principles. The point is not merely knowing what continuity means informally, but proving statements about limits and continuous functions with exact hypotheses.
This is where many students feel the course become more conceptual. The class moves from local ideas to global ones, asking when one delta must work everywhere and how closedness or compactness changes what continuous functions can do.
The later part of the course usually returns to derivatives, but now in theorem-proof form. Results such as Rolle's Theorem and the Mean Value Theorem become consequences of the earlier framework rather than accepted tools from calculus.
Public Rutgers discussion treats Math 311 as a real proof course rather than a continuation of plug-and-chug calculus. Students tend to say the course is manageable with steady practice, but only if you actively write proofs and do not rely on passive review.
Real analysis is where results that once felt automatic start to depend on exact assumptions such as compactness, continuity, or differentiability.
The epsilon-delta or epsilon-N format is how the course captures closeness and limiting behavior in a way that can actually be proved.
Continuity at each point does not automatically give one uniform rule on an entire set, which is why compactness and uniform continuity matter.
A correct intuition only becomes a solution when the proof identifies the needed theorem, quantifiers, and inequalities clearly enough for someone else to verify.
Common pitfall
Instead
Attach each theorem to the exact conditions under which it is valid, especially compactness, boundedness, continuity, and differentiability.
Common pitfall
Instead
Start by asking what the statement means in definition form and what kind of estimate or contradiction would prove it.
Common pitfall
Instead
Give yourself time to struggle productively, because that is where the skill of choosing a proof strategy gets built.
Common pitfall
Instead
Whenever you write 'gets close' or 'small enough,' translate that phrase into a formal bound.
3 open · Livingston
| Section | Status | Instructor | Meeting | Campus |
|---|---|---|---|---|
| 0115942 | Closed | Monday 8:30 AM-9:50 AM at TIL 209; Thursday 8:30 AM-9:50 AM at TIL 209; Tuesday 12:10 PM-1:30 PM at LSH A121TIL 209LSH A121 | Livingston | |
| 0315944 | Open | Tuesday 3:50 PM-5:10 PM at TIL 230; Thursday 3:50 PM-5:10 PM at TIL 230; Wednesday 2:00 PM-3:20 PM at BE 221TIL 230BE 221 | Livingston | |
| 0415945 | Open | Monday 7:30 PM-8:50 PM at LSH B105; Wednesday 7:30 PM-8:50 PM at LSH B105; Tuesday 5:40 PM-7:00 PM at TIL 230LSH B105TIL 230 | Livingston | |
| H115946 | Open | Monday 12:10 PM-1:30 PM at TIL 230; Thursday 12:10 PM-1:30 PM at TIL 230; Tuesday 10:20 AM-11:40 AM at BE 111TIL 230BE 111 | Livingston |
Historical student surveys
Teaching
4.34
Course quality
4.24
Response rate
45.8%
Coverage
119 offerings · 2014–2025
| Instructor | Offerings | Teaching | Quality |
|---|---|---|---|
| Xiaojun Huang | 9 | 4.42 | 4.43 |
| Fioralba Cakoni | 5 | 4.42 | 4.22 |
| Xiaochun Rong | 5 | 4.02 | 4.00 |
| Huang Xiaojun | 4 | 4.50 | 4.68 |
| Robert Beals | 4 | 4.75 | 4.53 |
| Gavin Stewart | 4 | 4.30 | 4.08 |
Catalog and planning context
Credits
4
Current campuses
Livingston
Current availability
3 open of 4
Catalog terms
Fall, Spring, Summer
Core codes
None listed
Loaded terms
6
(01:640:244 and 01:640:300 and 01:640:300 and 01:640:300) <em> OR </em> (01:640:252 and 01:640:300 and 01:640:300 and 01:640:300) <em> OR </em> (01:640:292 and 01:640:300 and 01:640:300 and 01:640:300) <em> OR </em> (21:640:314 and 01:640:250 and 01:640:300 and 01:640:300) <em> OR </em> (21:640:314 and 21:640:350 and 01:640:300 and 01:640:300)
No direct degree-list membership appears in the checked-in requirement index.