Who this is for

Route A: Career changers
You can code already or you have engineering experience but robotics maths feels fragmented. You want the minimum set that makes robotics concepts click.

Route B: Students & recent graduates
You have seen some of this in lectures but you want job ready fluency plus interview confidence.

Same topics for both routes. Route A learns best by building first. Route B often benefits from connecting concepts to textbook structure plus real systems.

The only maths topics you actually need for robotics jobs

1) Linear algebra for frames, transforms & vectors

Robotics is coordinate frames all day. Most “hard” robotics maths becomes manageable once you treat everything as vectors plus matrices with clear shapes.

What you actually need

• vectors, dot product, norms

• matrices, multiplication, transpose

• how to interpret a matrix as a transform

• homogeneous transforms (4×4) at an intuition level

• Jacobians as “how a small change here moves things there” at an intuition level

A strong structured path is Modern Robotics: Mechanics, Planning & Control which covers rigid body motion plus kinematics in a very robotics-native way. Hades

Where it shows up

• forward kinematics

• inverse kinematics

• mapping sensor measurements into a robot frame

• manipulating pose data in a codebase

2) Rotations without fear: trig, matrices, quaternions

A lot of robotics pain is rotation confusion. Once you are comfortable with representations, your confidence jumps.

What you actually need

• basic trig for angles plus sine/cosine intuition

• rotation matrices as “rotate a vector”

• Euler angles awareness plus why they can be awkward

• quaternions as a stable representation you can use without deriving

Where it shows up

• IMU orientation

• robot base to camera transforms

• localisation plus mapping

• motion planning constraints

Practical tip for interviews: you do not need to derive quaternions. You do need to explain why they are commonly used for 3D rotation representation in systems.

3) Kinematics as the core robotics skill

Kinematics is the maths of motion without worrying about forces. For many robotics software jobs, kinematics is more important than dynamics.

What you actually need

• forward kinematics conceptually

• inverse kinematics conceptually

• velocity kinematics via Jacobians at a high level

• constraints plus workspace intuition

MIT OpenCourseWare’s Introduction to Robotics covers kinematics plus dynamics plus control topics which is great for building a coherent mental model. MIT OpenCourseWare

Where it shows up

• robot arm manipulation

• mobile robot motion models

• calibration workflows

• building a simulator or debug tooling

4) Control basics: you do not need to be a control theorist

Many robotics roles involve control even if the job title is “software”. The goal is not to do advanced proofs. The goal is to understand the feedback loop.

What you actually need

• what a feedback controller is doing

• PID control intuition: P, I, D effects

• stability intuition: why too much gain causes oscillation

• discrete time thinking: sampling rate matters

MIT OCW’s robotics course explicitly includes control design plus actuators plus sensors which is useful context for why control maths matters in practice. MIT OpenCourseWare

Where it shows up

• motor control loops

• following a trajectory smoothly

• stabilising a drone or mobile platform behaviour

• tuning controllers during integration

5) Probability for robotics: uncertainty is the default

Robots operate with noisy sensors plus imperfect models. That is why probability shows up everywhere in localisation, mapping, tracking, sensor fusion, autonomy.

What you actually need

• Gaussian intuition: mean plus variance

• conditional probability intuition

• Bayes filter idea at a high level

• Kalman filter intuition: belief as a Gaussian updated by motion plus measurement

• why outliers break naive assumptions

Probabilistic Robotics is a classic reference for these ideas across localisation plus mapping plus tracking. gaoyichao.com
Thrun’s paper also frames Kalman filters within probabilistic algorithms used in robotics for tracking. cs.cmu.edu

Where it shows up

• sensor fusion with IMU plus wheel odometry plus GPS

• object tracking

• SLAM pipelines

• deciding how confident the robot is before acting

6) Optimisation for planning, estimation & tuning

A surprising amount of robotics is optimisation with constraints. Trajectory planning, parameter fitting, calibration, SLAM back end optimisation all live here.

What you actually need

• gradients at an intuition level

• cost functions: “what you are trying to minimise”

• constraints: what must never be violated

• local minima awareness: optimisation can get stuck

This topic also connects tightly to ML enabled robotics where training itself is optimisation.

7) Discrete maths for graphs in SLAM plus planning

You do not need a pure discrete maths course. You do need graph intuition because many robotics systems use graphs.

What you actually need

• nodes plus edges concepts

• path search intuition

• pose graphs conceptually for SLAM style thinking

Where it shows up:

• path planning on maps

• pose graph optimisation

• dependency graphs in robot software stacks

A 6 week maths plan for robotics jobs

Aim for 4–5 sessions per week of 45–60 minutes. Each week produces something you can put on GitHub.

Week 1: Vectors, frames & transforms

Learn

• vectors, dot products, norms

• frames as “where am I measuring from”

• rotation matrix intuition

Build

• a notebook that transforms points between frames

• a short README explaining frame conventions

Resources

• Modern Robotics preprint PDF for rigid body motion foundations Hades

Week 2: Rotations in 2D plus 3D

Learn

• 2D rotation matrix behaviour

• Euler angles pitfalls awareness

• quaternion usage basics

Build

• write small functions that convert between rotation matrix plus quaternion using a library

• generate test cases to confirm sanity

Week 3: Kinematics mini sprint

Learn

• forward kinematics for a simple arm

• inverse kinematics as a solve problem

• Jacobian intuition for small motions

Build

• 2 link planar arm FK plus IK

• plot reachable workspace

Resources

• MIT OCW Introduction to Robotics lecture notes for kinematics chapters MIT OpenCourseWare

• Modern Robotics for a structured kinematics path Hades

Week 4: Control basics that actually helps you integrate robots

Learn

• feedback loop intuition

• PID effects plus tuning habits

• sampling rate impact

Build

• a simple simulator where a PID controller tracks a target position

• a short tuning report: what changed when you altered P vs I vs D

Resource

• MIT OCW robotics overview includes control plus actuators plus sensors context MIT OpenCourseWare

Week 5: Probability for localisation plus tracking

Learn

• Gaussian noise intuition

• Bayes update conceptually

• Kalman filter intuition

Build

• 1D Kalman filter example then extend to 2D position tracking

• show how filter behaves under higher noise

Resources

• Probabilistic Robotics reference gaoyichao.com

• Thrun’s probabilistic algorithms paper for Kalman filter framing cs.cmu.edu

Week 6: Capstone project that looks like a real robotics portfolio

Pick one of these based on your target roles:

1. Mobile robot localisation demo
   motion model + noisy measurements + Kalman filter tracking

2. Manipulator kinematics tool
   FK plus IK + trajectory interpolation + visualisation

3. Perception plus tracking mini pipeline
   simple detector output + Kalman tracker + evaluation

4. ROS 2 mini stack
   publish sensor data + subscribe + compute a transform + visualise

If you want ROS 2 evidence on your CV, follow the ROS 2 tutorials for topics plus workspace builds using colcon. docs.ros.org

Portfolio projects that prove the maths for robotics jobs

Project 1: Robot arm FK plus IK demo

Shows

• linear algebra

• kinematics intuition

• clear explanation of assumptions

Add

• plots of workspace

• tests for edge cases

Project 2: PID tracking simulator

Shows

• control loop intuition

• ability to tune without guessing

Add

• a short report explaining how you tuned P, I, D

Project 3: Kalman filter localisation notebook

Shows

• probability thinking

• sensor fusion mindset

Anchor references

• Probabilistic Robotics gaoyichao.com

• Kalman filter within probabilistic robotics methods cs.cmu.edu

Project 4: ROS 2 pub/sub robotics mini app

Shows

• you can work in the ecosystem most employers recognise

• you understand data flow between nodes

Resources

• ROS 2 topics tutorial docs.ros.org

• ROS 2 colcon build tutorial docs.ros.org

• ROS 2 tutorials index docs.ros.org

How to write these maths skills on your CV

Swap vague claims for proof like:

• Built forward plus inverse kinematics tooling for a planar manipulator with clear frame conventions plus test coverage Hades

• Implemented a PID tracking simulator plus produced a tuning note explaining stability plus overshoot trade-offs MIT OpenCourseWare

• Implemented a Kalman filter based localisation demo showing behaviour under different noise conditions gaoyichao.com

• Built a ROS 2 publisher/subscriber mini stack using topics plus colcon workflows docs.ros.org

Resources section

Robotics maths foundations

• Modern Robotics: Mechanics, Planning & Control free preprint PDF Hades

• MIT OpenCourseWare Introduction to Robotics course plus lecture notes MIT OpenCourse

Probability, localisation, SLAM thinking

• Probabilistic Robotics reference text ACM Digital Library

• Thrun paper on probabilistic algorithms in robotics including Kalman filter framing cs.cmu.edu

ROS 2 for real world portfolio evidence

• ROS 2 tutorial on topics docs.ros.org

• ROS 2 tutorial on building workspaces with colcon docs.ros.org

• ROS 2 tutorials index docs.ros.org