Math 120 is UBC's honours differential calculus course—designed for students planning to major in mathematics or pursue mathematically rigorous programs. It covers the same topics as Math 100 (limits, derivatives, applications), but with far greater depth, theoretical rigor, and proof-based reasoning. If you're comfortable with abstraction, enjoy mathematical reasoning, and want a challenging introduction to calculus, Math 120 is the right choice. But be prepared: this isn't just "harder Math 100." It's a fundamentally different approach to learning calculus.
What is covered in UBC Math 120?
Math 120 introduces differential calculus with theoretical rigor and proof-based learning. Topics include:
- Real numbers and sequences: Axioms, completeness, and convergence proofs
- Limits and continuity: Rigorous epsilon-delta definitions and proofs of limit theorems
- Derivatives: Definition using limits, proofs of differentiation rules (power, product, quotient, chain rule)
- Mean Value Theorem: Statement, proof, and applications to understanding function behavior
- Applications of derivatives: Optimization, curve sketching, and L'Hôpital's Rule with theoretical justifications
- Taylor polynomials and approximations: Using derivatives to approximate functions
- Exponential and logarithmic functions: Rigorous definitions, properties, and proofs
- Introduction to proof techniques: Direct proof, proof by contradiction, and induction
Math 120 is typically followed by Math 121 (Honours Integral Calculus) and is strongly recommended for students planning to major in mathematics.
Common challenges students face in Math 120
Proofs dominate the course
Unlike Math 100, where you mostly compute answers, Math 120 asks you to prove theorems, justify every step, and understand the logical structure of calculus. If you've never written proofs before, the learning curve is steep.
Abstract thinking is required
You're not just finding derivatives—you're proving why differentiation rules work. You need to think abstractly about functions, limits, and continuity, not just apply formulas.
The pace is fast
Honours courses move quickly. You're expected to absorb dense material, complete challenging problem sets, and keep up with rigorous lectures—all while learning to write mathematical proofs.
Exams test deep understanding
You can't memorize your way through Math 120. Exams ask you to prove unfamiliar results, justify your reasoning, and apply concepts in novel ways.
How Learn4Less helps you succeed in Math 120
Our tutors have strong mathematical backgrounds and understand the theoretical demands of honours calculus.
Proof-writing guidance
We teach you how to structure proofs, choose the right approach (direct, contradiction, induction), and write clear, logical arguments. You'll learn to think like a mathematician.
Conceptual clarity
We help you understand the *why* behind theorems: why the Mean Value Theorem matters, why epsilon-delta definitions are necessary, and how Taylor polynomials connect to function behavior.
Problem-solving strategies
Honours problems aren't routine. We teach you how to approach unfamiliar questions, break them into manageable parts, and apply core concepts creatively.
Math 120 exam and midterm preparation
Math 120 typically has two midterms and a final exam, all heavily proof-based. Here's how we prepare you:
Practice with past exams
We work through previous years' exams so you understand the level of rigor expected. You'll practice writing proofs under time pressure.
Core theorem mastery
Theorems like the Mean Value Theorem, Intermediate Value Theorem, and limit theorems appear frequently. We ensure you understand them deeply, not just memorize statements.
Time management for proofs
Proof-based exams require different time management than computational exams. We teach you how to allocate time, when to sketch arguments, and how to maximize partial credit.
Why choose Learn4Less for Math 120 tutoring?
Strong mathematical backgrounds
Our tutors have experience with honours-level mathematics and understand the theoretical demands of Math 120. We've helped many honours students succeed.
Familiar with UBC honours courses
We know UBC's Math 120 syllabus, typical textbooks (like *Calculus* by Spivak or *Real Mathematical Analysis* by Pugh), and the proof-based exam style.
Flexible learning options
Choose in-person tutoring near UBC or online sessions. Need help before a specific midterm? Book a targeted prep session. Want consistent support? Weekly tutoring helps you stay on top of problem sets and proofs.
Video study packages
Our video packages cover key Math 120 topics with proof walkthroughs—perfect for reviewing before exams.
Frequently Asked Questions
What's the difference between Math 120 and Math 100?
Math 120 is the honours version, focusing on rigorous proofs, epsilon-delta definitions, and theoretical foundations. Math 100 is more computational, emphasizing applications and problem-solving. Math 120 is for students planning to major in mathematics or who enjoy abstraction.
Do I need Math 120 to major in mathematics at UBC?
Not strictly required, but strongly recommended. Math 120/121 prepares you for upper-level proof-based courses much better than Math 100/101. If you're serious about mathematics, take the honours sequence.
Is Math 120 a lot harder than Math 100?
Yes. Math 120 demands proof-writing skills, abstract thinking, and deeper conceptual understanding. It's designed for students who enjoy mathematical rigor and are comfortable with challenging, theoretical coursework.
Can I switch from Math 120 to Math 100?
Yes, especially in the first few weeks. If you find Math 120 too abstract or proof-heavy, you can drop down to Math 100. Talk to your advisor early if you're struggling.
When should I get a tutor for Math 120?
Honours students often benefit from tutoring right from the start. The proof-writing skills take time to develop, and falling behind in an honours course is hard to recover from. Proactive support helps you build strong foundations early.