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lecture note
Not too much in this lecture if you know the basic knowledge about optimization. From my perspective, the most important thing is about(Gradient check).

In the Open Course UFLDL, it also introduces gradient check, you can learn from here

Gradient check: numerically checking the derivatives computed by your code to make sure that your implementation is correct. Code in python

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def eval_numerical_gradient(f, x):
  """ 
  a naive implementation of numerical gradient of f at x 
  - f should be a function that takes a single argument
  - x is the point (numpy array) to evaluate the gradient at
  """ 

  fx = f(x) # evaluate function value at original point
  grad = np.zeros(x.shape)
  h = 0.00001

  # iterate over all indexes in x
  it = np.nditer(x, flags=['multi_index'], op_flags=['readwrite'])
  while not it.finished:

    # evaluate function at x+h
    ix = it.multi_index
    old_value = x[ix]
    x[ix] = old_value + h # increment by h
    fxh = f(x) # evalute f(x + h)
    x[ix] = old_value # restore to previous value (very important!)

    # compute the partial derivative
    grad[ix] = (fxh - fx) / h # the slope
    it.iternext() # step to next dimension

  return grad

Mini-batch gradient descent
Stochastic Gradient Descent (SGD): usually for update the weight one sample a time. But now some people also use it to describe Mini-batch gradient descent

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