When you look up a solution, don’t read the whole thing. Read only the first sentence or hint. For Lang’s problems, the key is often a clever observation (e.g., “Consider the kernel of the homomorphism φ”). Try to complete the proof yourself after that hint.
In the modern era, many students undertake "Lang Projects"—attempting to solve every problem in a text and publishing their work on a blog or a GitHub repository.
Lang is famous for exercises like: “Let H be a subgroup of G such that the index [G:H] = 2. Prove H is normal.” lang undergraduate algebra solutions
: Highly accurate; follows Lang’s specific notation and style.
Professors are aware of online . They often modify Lang’s problems slightly to thwart copy-paste cheating. Here is the ethical line: When you look up a solution, don’t read the whole thing
Mathematics is learned by doing. If you bypass the struggle, you only fool yourself.
Many elite universities (MIT, Harvard, UC Berkeley) have used Lang for their honors algebra sequence. Search for: Try to complete the proof yourself after that hint
If you’re stuck on a proof or just want to verify your work, here is the best way to navigate the landscape of Lang solutions. The Reality of "Official" Solutions
Now go pick up your pencil. And when you get stuck—you know where to look.
When stuck on a Lang exercise, find the corresponding theorem in Dummit & Foote and see their worked proof.
Many graduate students and professors post their personal solution sets online. : Look for LaTeX-formatted PDFs on GitHub.